Year 4: Turns and right angles
Part of the Year 4 shapes, angles and symmetry chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Turns and right angles
When you spin round on the spot, you make a turn. A whole turn takes you all the way round until you face the way you started. A half turn takes you half the way round, so you face the opposite way. A quarter turn is one quarter of the way round, like turning to look at the door beside you. A three-quarter turn is three quarters of the way round.
An angle is the amount of turn between two lines that meet at a point. The corner of a book, a door or a window makes a very special angle. It is called a right angle. A right angle is a quarter turn. We mark a right angle with a small square.
A whole turn is made from 4 right angles. So a half turn is 2 right angles, and two right angles together make a straight line. A three-quarter turn is 3 right angles.
| Turn | Fraction of a whole turn | Right angles |
|---|---|---|
| quarter turn | 14 | 1 |
| half turn | 12 | 2 (a straight line) |
| three-quarter turn | 34 | 3 |
| whole turn | 1 | 4 |
Clockwise and anticlockwise. Clockwise is the way the hands of a clock go. Anticlockwise is the other way. On a compass, going clockwise from North you reach East, then South, then West, then North again. Each step is a quarter turn.
Perpendicular and parallel lines. Two lines that meet at a right angle are perpendicular. Two lines that stay the same distance apart and never meet are parallel.
Key ideas
- A whole turn = 4 right angles. A half turn = 2 right angles. A quarter turn = 1 right angle. A three-quarter turn = 3 right angles.
- A right angle is a quarter turn. It looks like the corner of a book. It is marked with a small square.
- Two right angles make a straight line.
- Clockwise goes the way the hands of a clock go. Anticlockwise goes the other way.
- Lines that meet at a right angle are perpendicular. Lines that never meet are parallel.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. The numbers 12, 3, 6 and 9 on a clock are a quarter turn apart. Count the quarter turns the minute hand makes as it moves clockwise.
- Find the start and the end. We look at where the hand starts and where it stops.It starts at 12 and moves clockwise to 6.
- Count the quarter turns. Each jump from one of 12, 3, 6, 9 to the next is a quarter turn.12 → 3 → 6
2 quarter turns - Name the turn. 2 out of 4 quarters.It is a half turn (2 right angles).
Check. A whole turn takes 60 minutes. A half turn takes 30 minutes. ✓
Watch out. The minute hand always moves clockwise.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Turn one step at a time. Remember the order of the compass points going clockwise: North, East, South, West. A quarter turn clockwise moves one place along.
- Remember the order of the compass points going clockwise. A quarter turn clockwise moves one place along: N, E, S, W. Anticlockwise goes the other way.North → East → South → West → North
- Turn a quarter turn anticlockwise. 1 quarter turn. Clockwise goes N → E → S → W → N. Anticlockwise goes the other way.Start facing East.
East → North - Write the answer. The person is now facing North.
Check. Going clockwise, North = 0, East = 1, South = 2, West = 3 quarter turns from North. The total of the turns gives the same direction. ✓
Watch out. Clockwise: N → E → S → W. Anticlockwise is the opposite way, so N → W → S → E.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with the corner of a piece of paper. The corner of paper is a right angle.
- Put the corner of a piece of paper on the angle. Line up one side of the paper with one arm of the angle. The dashed lines show the paper corner.
- Look at the other arm. It tells us if the angle is the same as the paper corner, smaller, or bigger.The other arm lines up exactly with the other side of the paper corner.
- Answer. It is a right angle.
Check. A right angle is a quarter turn. ✓
Watch out. Look at the size of the opening, not the length of the arms.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Check each pair of lines. Perpendicular lines are lines that meet at a right angle.
- Remember what we are looking for. We want the pair that is perpendicular.Perpendicular lines meet at a right angle (a square corner).
- Look at each pair of lines. Decide if each pair is parallel, perpendicular or neither.A: parallel
B: perpendicular
C: neither - Choose the pair. Only pair B meets at a right angle.The perpendicular pair is B.
Check. Pair B is the only one that is perpendicular. ✓
Watch out. Lines that cross at an angle that is not a right angle are neither.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. A right angle is a quarter turn. A whole turn is 4 quarter turns. Count how many quarter turns make the turn you are asked about.
- Think about the whole turn. A whole turn is all the way round. It is made of 4 right angles.1 whole turn = 4 right angles
- Find how many quarters are in a three-quarter turn. A three-quarter turn is 3 out of the 4 quarter turns.three-quarter turn = 3 quarter turns
- Write the answer. Each quarter turn is one right angle.three-quarter turn = 3 right angles
Check. 3 out of 4 quarters is 34 of a whole turn. ✓
Watch out. A half turn is 2 right angles (a straight line), not 1.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Follow the arrow. Count how many quarter turns the pointer makes. A quarter turn is a right angle.
- Find where the pointer starts and where it ends. We say which way it points: up, right, down or left.Start: down.
End: left. - Follow the arrow and count the quarter turns. The arrow goes anticlockwise. Each time the pointer moves to the next of up, right, down and left, that is one quarter turn.down → right → up → left
That is 3 quarter turns. - Name the turn. 3 out of 4 quarters.It is a three-quarter turn anticlockwise.
- Write the number of right angles. Each quarter turn is one right angle.3 right angles
Check. 3 quarters out of 4 is 34 of a whole turn. ✓
Watch out. Count the quarter turns the arrow makes, not the number of directions you list.
Watch out
A half turn is 2 right angles, not 1. A right angle is a quarter turn. Two of them make a half turn (a straight line). Also, a clockwise turn and an anticlockwise turn of the same size end in different places, unless it is a half turn or a whole turn.Exercise 9A Turns, right angles and perpendicular lines
Non-calculatorKey words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. A right angle is a quarter turn. A whole turn is 4 quarter turns. Count how many quarter turns make the turn you are asked about.
- Think about the whole turn. A whole turn is all the way round. It is made of 4 right angles.1 whole turn = 4 right angles
- Find how many quarters are in a quarter turn. A quarter turn is 1 out of the 4 quarter turns.quarter turn = 1 quarter turn
- Write the answer. Each quarter turn is one right angle.quarter turn = 1 right angle
Check. 1 out of 4 quarters is 14 of a whole turn. ✓
Watch out. A half turn is 2 right angles (a straight line), not 1.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. A right angle is a quarter turn. A whole turn is 4 quarter turns. Count how many quarter turns make the turn you are asked about.
- Think about the whole turn. A whole turn is all the way round. It is made of 4 right angles.1 whole turn = 4 right angles
- Find how many quarters are in a half turn. A half turn is 2 out of the 4 quarter turns.half turn = 2 quarter turns
- Write the answer. Each quarter turn is one right angle.half turn = 2 right angles
Check. 2 out of 4 quarters is 12 of a whole turn. ✓
Watch out. A half turn is 2 right angles (a straight line), not 1.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. A right angle is a quarter turn. A whole turn is 4 quarter turns. Count how many quarter turns make the turn you are asked about.
- Think about the whole turn. A whole turn is all the way round. It is made of 4 right angles.1 whole turn = 4 right angles
- Find how many quarters are in a three-quarter turn. A three-quarter turn is 3 out of the 4 quarter turns.three-quarter turn = 3 quarter turns
- Write the answer. Each quarter turn is one right angle.three-quarter turn = 3 right angles
Check. 3 out of 4 quarters is 34 of a whole turn. ✓
Watch out. A half turn is 2 right angles (a straight line), not 1.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. A right angle is a quarter turn. A whole turn is 4 quarter turns. Count how many quarter turns make the turn you are asked about.
- Think about the whole turn. A whole turn is all the way round. It is made of 4 right angles.1 whole turn = 4 right angles
- Find how many quarters are in a whole turn. It is all 4 of the quarter turns.whole turn = 4 quarter turns
- Write the answer. Each quarter turn is one right angle.whole turn = 4 right angles
Check. 4 out of 4 quarters is 11 of a whole turn. ✓
Watch out. A half turn is 2 right angles (a straight line), not 1.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Follow the arrow. Count how many quarter turns the pointer makes. A quarter turn is a right angle.
- Find where the pointer starts and where it ends. We say which way it points: up, right, down or left.Start: up.
End: right. - Follow the arrow and count the quarter turns. The arrow goes clockwise. Each time the pointer moves to the next of up, right, down and left, that is one quarter turn.up → right
That is 1 quarter turn. - Name the turn. 1 out of 4 quarters.It is a quarter turn clockwise.
Check. 1 quarters out of 4 is 14 of a whole turn. ✓
Watch out. Count the quarter turns the arrow makes, not the number of directions you list.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Follow the arrow. Count how many quarter turns the pointer makes. A quarter turn is a right angle.
- Find where the pointer starts and where it ends. We say which way it points: up, right, down or left.Start: right.
End: left. - Follow the arrow and count the quarter turns. The arrow goes clockwise. Each time the pointer moves to the next of up, right, down and left, that is one quarter turn.right → down → left
That is 2 quarter turns. - Name the turn. 2 out of 4 quarters.It is a half turn clockwise.
Check. 2 quarters out of 4 is 12 of a whole turn. ✓
Watch out. Count the quarter turns the arrow makes, not the number of directions you list.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Follow the arrow. Count how many quarter turns the pointer makes. A quarter turn is a right angle.
- Find where the pointer starts and where it ends. We say which way it points: up, right, down or left.Start: down.
End: left. - Follow the arrow and count the quarter turns. The arrow goes anticlockwise. Each time the pointer moves to the next of up, right, down and left, that is one quarter turn.down → right → up → left
That is 3 quarter turns. - Name the turn. 3 out of 4 quarters.It is a three-quarter turn anticlockwise.
Check. 3 quarters out of 4 is 34 of a whole turn. ✓
Watch out. Count the quarter turns the arrow makes, not the number of directions you list.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Follow the arrow. Count how many quarter turns the pointer makes. A quarter turn is a right angle.
- Find where the pointer starts and where it ends. We say which way it points: up, right, down or left.It starts pointing left and ends pointing left again.
- Follow the arrow and count the quarter turns. The arrow goes clockwise. Each time the pointer moves to the next of up, right, down and left, that is one quarter turn.left → up → right → down → left
That is 4 quarter turns. - Name the turn. 4 out of 4 quarters.It is a whole turn.
Check. 4 quarters out of 4 is 11 of a whole turn. ✓
Watch out. Count the quarter turns the arrow makes, not the number of directions you list.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Turn one step at a time. Remember the order of the compass points going clockwise: North, East, South, West. A quarter turn clockwise moves one place along.
- Remember the order of the compass points going clockwise. A quarter turn clockwise moves one place along: N, E, S, W. Anticlockwise goes the other way.North → East → South → West → North
- Turn a quarter turn clockwise. 1 quarter turn. Clockwise goes N → E → S → W → N. Anticlockwise goes the other way.Start facing North.
North → East - Write the answer. The person is now facing East.
Check. Going clockwise, North = 0, East = 1, South = 2, West = 3 quarter turns from North. The total of the turns gives the same direction. ✓
Watch out. Clockwise: N → E → S → W. Anticlockwise is the opposite way, so N → W → S → E.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Turn one step at a time. Remember the order of the compass points going clockwise: North, East, South, West. A quarter turn clockwise moves one place along.
- Remember the order of the compass points going clockwise. A quarter turn clockwise moves one place along: N, E, S, W. Anticlockwise goes the other way.North → East → South → West → North
- Turn a half turn clockwise. 2 quarter turns. Clockwise goes N → E → S → W → N. Anticlockwise goes the other way.Start facing South.
South → West → North - Write the answer. The person is now facing North.
Check. Going clockwise, North = 0, East = 1, South = 2, West = 3 quarter turns from North. The total of the turns gives the same direction. ✓
Watch out. Clockwise: N → E → S → W. Anticlockwise is the opposite way, so N → W → S → E.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Turn one step at a time. Remember the order of the compass points going clockwise: North, East, South, West. A quarter turn clockwise moves one place along.
- Remember the order of the compass points going clockwise. A quarter turn clockwise moves one place along: N, E, S, W. Anticlockwise goes the other way.North → East → South → West → North
- Turn a quarter turn anticlockwise. 1 quarter turn. Clockwise goes N → E → S → W → N. Anticlockwise goes the other way.Start facing West.
West → South - Write the answer. The person is now facing South.
Check. Going clockwise, North = 0, East = 1, South = 2, West = 3 quarter turns from North. The total of the turns gives the same direction. ✓
Watch out. Clockwise: N → E → S → W. Anticlockwise is the opposite way, so N → W → S → E.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Turn one step at a time. Remember the order of the compass points going clockwise: North, East, South, West. A quarter turn clockwise moves one place along.
- Remember the order of the compass points going clockwise. A quarter turn clockwise moves one place along: N, E, S, W. Anticlockwise goes the other way.North → East → South → West → North
- Turn a three-quarter turn clockwise. 3 quarter turns. Clockwise goes N → E → S → W → N. Anticlockwise goes the other way.Start facing East.
East → South → West → North - Write the answer. The person is now facing North.
Check. Going clockwise, North = 0, East = 1, South = 2, West = 3 quarter turns from North. The total of the turns gives the same direction. ✓
Watch out. Clockwise: N → E → S → W. Anticlockwise is the opposite way, so N → W → S → E.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. The numbers 12, 3, 6 and 9 on a clock are a quarter turn apart. Count the quarter turns the minute hand makes as it moves clockwise.
- Find the start and the end. We look at where the hand starts and where it stops.It starts at 12 and moves clockwise to 3.
- Count the quarter turns. Each jump from one of 12, 3, 6, 9 to the next is a quarter turn.12 → 3
1 quarter turn - Name the turn. 1 out of 4 quarters.It is a quarter turn (1 right angle).
Check. A whole turn takes 60 minutes. A quarter turn takes 15 minutes. ✓
Watch out. The minute hand always moves clockwise.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. The numbers 12, 3, 6 and 9 on a clock are a quarter turn apart. Count the quarter turns the minute hand makes as it moves clockwise.
- Find the start and the end. We look at where the hand starts and where it stops.It starts at 3 and moves clockwise to 9.
- Count the quarter turns. Each jump from one of 12, 3, 6, 9 to the next is a quarter turn.3 → 6 → 9
2 quarter turns - Name the turn. 2 out of 4 quarters.It is a half turn (2 right angles).
Check. A whole turn takes 60 minutes. A half turn takes 30 minutes. ✓
Watch out. The minute hand always moves clockwise.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. The numbers 12, 3, 6 and 9 on a clock are a quarter turn apart. Count the quarter turns the minute hand makes as it moves clockwise.
- Find the start and the end. We look at where the hand starts and where it stops.It starts at 9 and moves clockwise to 12.
- Count the quarter turns. Each jump from one of 12, 3, 6, 9 to the next is a quarter turn.9 → 12
1 quarter turn - Name the turn. 1 out of 4 quarters.It is a quarter turn (1 right angle).
Check. A whole turn takes 60 minutes. A quarter turn takes 15 minutes. ✓
Watch out. The minute hand always moves clockwise.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. The numbers 12, 3, 6 and 9 on a clock are a quarter turn apart. Count the quarter turns the minute hand makes as it moves clockwise.
- Find the start and the end. We look at where the hand starts and where it stops.It starts at 6 and moves clockwise to 6.
- Count the quarter turns. It goes all the way round and comes back to the start.6 → 9 → 12 → 3 → 6
4 quarter turns - Name the turn. 4 out of 4 quarters.It is a whole turn (4 right angles).
Check. A whole turn takes 60 minutes. A whole turn takes 60 minutes. ✓
Watch out. The minute hand always moves clockwise.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with the corner of a piece of paper. The corner of paper is a right angle.
- Put the corner of a piece of paper on the angle. Line up one side of the paper with one arm of the angle. The dashed lines show the paper corner.
- Look at the other arm. It tells us if the angle is the same as the paper corner, smaller, or bigger.The other arm lines up exactly with the other side of the paper corner.
- Answer. It is a right angle.
Check. A right angle is a quarter turn. ✓
Watch out. Look at the size of the opening, not the length of the arms.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with the corner of a piece of paper. The corner of paper is a right angle.
- Put the corner of a piece of paper on the angle. Line up one side of the paper with one arm of the angle. The dashed lines show the paper corner.
- Look at the other arm. It tells us if the angle is the same as the paper corner, smaller, or bigger.The other arm is inside the paper corner (there is a gap).
- Answer. The angle is smaller than a right angle, so it is not a right angle.
Check. A right angle is a quarter turn. ✓
Watch out. Look at the size of the opening, not the length of the arms.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with the corner of a piece of paper. The corner of paper is a right angle.
- Put the corner of a piece of paper on the angle. Line up one side of the paper with one arm of the angle. The dashed lines show the paper corner.
- Look at the other arm. It tells us if the angle is the same as the paper corner, smaller, or bigger.The other arm lines up exactly with the other side of the paper corner.
- Answer. It is a right angle.
Check. A right angle is a quarter turn. ✓
Watch out. Look at the size of the opening, not the length of the arms.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Compare the angle with the corner of a piece of paper. The corner of paper is a right angle.
- Put the corner of a piece of paper on the angle. Line up one side of the paper with one arm of the angle. The dashed lines show the paper corner.
- Look at the other arm. It tells us if the angle is the same as the paper corner, smaller, or bigger.The other arm is outside the paper corner (it sticks out past it).
- Answer. The angle is bigger than a right angle, so it is not a right angle.
Check. A right angle is a quarter turn. ✓
Watch out. Look at the size of the opening, not the length of the arms.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Check each pair of lines. Perpendicular lines are lines that meet at a right angle.
- Remember what we are looking for. We want the pair that is perpendicular.Perpendicular lines meet at a right angle (a square corner).
- Look at each pair of lines. Decide if each pair is parallel, perpendicular or neither.A: parallel
B: neither
C: perpendicular - Choose the pair. Only pair C meets at a right angle.The perpendicular pair is C.
Check. Pair C is the only one that is perpendicular. ✓
Watch out. Lines that cross at an angle that is not a right angle are neither.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Check each pair of lines. Parallel lines are the same distance apart and never meet.
- Remember what we are looking for. We want the pair that is parallel.Parallel lines stay the same distance apart and never meet.
- Look at each pair of lines. Decide if each pair is parallel, perpendicular or neither.A: neither
B: parallel
C: perpendicular - Choose the pair. Only pair B has two lines that stay the same distance apart.The parallel pair is B.
Check. Pair B is the only one that is parallel. ✓
Watch out. Lines that cross at an angle that is not a right angle are neither.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Parallel lines never meet and stay the same distance apart. Perpendicular lines meet at a right angle.
- Look at where the lines cross. Lines that meet at a right angle are perpendicular. The little square shows the right angle.The lines cross and make a square corner.
- Test with the corner of paper. A paper corner fits exactly in the angle.It is a right angle.
- Answer. The lines are perpendicular.
Check. Test: only perpendicular lines make a right angle, and only parallel lines never meet. ✓
Watch out. Lines that cross but not at a right angle are neither parallel nor perpendicular.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Parallel lines never meet and stay the same distance apart. Perpendicular lines meet at a right angle.
- Look at the two lines. Parallel lines are always the same distance apart. They would never meet, even if they went on for ever.The lines go the same way and the gap between them stays the same.
- Check for a right angle. Perpendicular lines meet at a right angle.The lines do not cross, so there is no right angle.
- Answer. The lines are parallel.
Check. Test: only perpendicular lines make a right angle, and only parallel lines never meet. ✓
Watch out. Lines that cross but not at a right angle are neither parallel nor perpendicular.
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Parallel lines never meet and stay the same distance apart. Perpendicular lines meet at a right angle.
- Look at where the lines cross. Perpendicular lines cross at a right angle.The lines cross, but the angle is not a square corner: it is smaller than a right angle.
- Check for parallel. Parallel lines never meet.These lines cross each other, so they are not parallel.
- Answer. The lines are neither parallel nor perpendicular.
Check. Test: only perpendicular lines make a right angle, and only parallel lines never meet. ✓
Watch out. Lines that cross but not at a right angle are neither parallel nor perpendicular.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Test each corner (vertex) of the shape against the corner of a piece of paper. Count the corners that fit it exactly.
- Look at each corner of the shape. The small squares in this picture show the right angles.
- Test every corner. Corners that are smaller or bigger than a paper corner are not right angles.A: right angle
B: right angle
C: right angle
D: right angle - Count the right angles. The rectangle has 4 right angles.
Check. Count the little squares in the picture: 4. ✓
Watch out. A corner that looks bigger than two right angles (pointing inwards) is not a right angle either.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Test each corner (vertex) of the shape against the corner of a piece of paper. Count the corners that fit it exactly.
- Look at each corner of the shape. The small squares in this picture show the right angles.
- Test every corner. Corners that are smaller or bigger than a paper corner are not right angles.A: right angle
B: smaller than a right angle
C: smaller than a right angle - Count the right angles. The right-angled triangle has 1 right angle.
Check. Count the little squares in the picture: 1. ✓
Watch out. A corner that looks bigger than two right angles (pointing inwards) is not a right angle either.
Key words. An angle is the amount of turn between two lines that meet. An acute angle is smaller than a right angle. An obtuse angle is bigger than a right angle but smaller than a straight line. A straight line is two right angles.
Method. Test each corner (vertex) of the shape against the corner of a piece of paper. Count the corners that fit it exactly.
- Look at each corner of the shape. The small squares in this picture show the right angles.
- Test every corner. Corners that are smaller or bigger than a paper corner are not right angles.A: right angle
B: right angle
C: bigger than a right angle
D: smaller than a right angle
E: bigger than a right angle - Count the right angles. The house shape has 2 right angles.
Check. Count the little squares in the picture: 2. ✓
Watch out. A corner that looks bigger than two right angles (pointing inwards) is not a right angle either.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Turn one step at a time. Remember the order of the compass points going clockwise: North, East, South, West. A quarter turn clockwise moves one place along.
- Remember the order of the compass points going clockwise. A quarter turn clockwise moves one place along: N, E, S, W. Anticlockwise goes the other way.North → East → South → West → North
- Turn a quarter turn clockwise. 1 quarter turn. Clockwise goes N → E → S → W → N. Anticlockwise goes the other way.Start facing North.
North → East - Turn a half turn clockwise. 2 quarter turns. Clockwise goes N → E → S → W → N. Anticlockwise goes the other way.Start facing East.
East → South → West - Turn a quarter turn anticlockwise. 1 quarter turn. Clockwise goes N → E → S → W → N. Anticlockwise goes the other way.Start facing West.
West → South - Write the answer. The person is now facing South.
Check. Going clockwise, North = 0, East = 1, South = 2, West = 3 quarter turns from North. The total of the turns gives the same direction. ✓
Watch out. Clockwise: N → E → S → W. Anticlockwise is the opposite way, so N → W → S → E.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. A whole turn is 4 right angles. Aisha has made 3 right angles. Find how many are left, and what fraction she has made.
- Write the whole turn in right angles. A whole turn is 4 right angles.4 right angles
- Find how many more she needs. Take away the 3 she has made.4 − 3 = 1 right angle
- Write the fraction she turned. She made 3 of the 4 quarter turns.3 out of 4 = 34 of a whole turn
Check. 3 + 1 = 4 right angles. ✓
Watch out. Each right angle is one quarter, so 3 right angles is three quarters, not three tenths.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. A half turn is two quarter turns. Tom has mixed up the half turn and the quarter turn.
- Look at what Tom said. Tom says a half turn is 1 right angle.Half turn = 1 right angle?
- Work out the right answer. A right angle is a quarter turn. A half turn is two quarter turns.half turn = quarter turn + quarter turn = 2 right angles
- Answer. No, Tom is wrong. A half turn is 2 right angles. It is a straight line.
Check. 2 right angles + 2 right angles = 4 right angles = a whole turn. So 2 is half of 4. ✓
Watch out. 1 right angle is the quarter turn.
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Two right angles together make a half turn, which is a straight line.
- Add two right angles. One right angle is a quarter turn.quarter turn + quarter turn = half turn
- Think about a half turn. A half turn is a straight line.Two right angles make a straight line.
- Decide. This is always true.
Check. Draw two corners of paper side by side: they make a straight edge. ✓
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Try some turns clockwise and anticlockwise. Does the pointer end in the same place?
- Try a quarter turn. Start facing North.Clockwise: East. Anticlockwise: West. Different places.
- Try a half turn. Start facing North.Clockwise: South. Anticlockwise: South. The same place.
- Decide. It happens for some turns but not for all of them.This is sometimes true.
Check. We found one turn where it is true and one where it is not. ✓
Key words. A quadrilateral has 4 straight sides. Parallel lines stay the same distance apart and never meet. Perpendicular lines meet at a right angle. A trapezium has exactly one pair of parallel sides.
Method. Perpendicular lines meet at a right angle. Parallel lines never meet.
- Think about parallel lines. They never meet, so there is no angle between them.Parallel lines never cross.
- Think about perpendicular lines. They cross at a right angle.Perpendicular lines always cross.
- Decide. A pair of lines cannot be both.This is never true.
Check. The lines in a pair either meet or never meet, not both. ✓
Key words. A right angle is a quarter turn, like the corner of a book. Two right angles make a half turn (a straight line). Three make a three-quarter turn. Four make a whole turn. Clockwise is the way the hands of a clock go. Anticlockwise is the other way.
Method. Do the two turns one after the other. Then add the quarter turns to find the total turn.
- First turn: three-quarter turn clockwise. Three quarter turns. Clockwise from West: W → N → E → S.Leo starts facing West and ends this turn facing South.
- Second turn: quarter turn clockwise. One more quarter turn clockwise from South.S → W. Leo now faces West.
- Add the turns to find the total. Count all the quarter turns.3 quarters + 1 quarter = 4 quarters = a whole turn (4 right angles).
Check. A whole turn brings you back to the start, and Leo started facing West. ✓
Watch out. Add the turns first: three quarters and one quarter make a whole turn, so he ends where he started.