Year 4: Triangles
Part of the Year 4 shapes, angles and symmetry chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Triangles
A triangle is a shape with 3 straight sides, 3 corners (also called vertices) and 3 angles. We name triangles by looking at their sides and their angles.
- An equilateral triangle has 3 equal sides. All three angles are equal too.
- An isosceles triangle has 2 equal sides. Two of its angles are equal too.
- A scalene triangle has no equal sides.
- A right-angled triangle has one right angle.
Tick marks. In a picture, sides with the same number of tick marks are equal. A right-angled triangle can be scalene (like the one above, with sides 3, 4 and 5) or isosceles (if two sides next to the right angle are equal).
A triangle looks different when you turn it round, but it is still the same triangle. An isosceles triangle can point up, down or sideways.
Key ideas
- Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides.
- Right-angled: has one right angle (shown by a small square).
- Tick marks show sides of equal length.
- An isosceles triangle has two equal angles. An equilateral triangle has three equal angles.
- Turning a triangle round does not change its name.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Tick marks show sides that are equal.All three sides have one tick mark, so all three sides are equal.
- Count the equal sides. The number of equal sides tells us the name.There are 3 equal sides.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has 3 equal sides: equilateral.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 3. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Sides that have the same length are equal.The sides are 8 cm, 5 cm and 5 cm.
- Count the equal sides. The number of equal sides tells us the name.There are 2 equal sides.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has 2 equal sides: isosceles.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 2. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Sides that have the same length are equal.The sides are 7 cm, 5 cm and 4 cm.
- Count the equal sides. The number of equal sides tells us the name.No two sides are equal.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has no equal sides: scalene.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 0. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Sides that have the same length are equal.The sides are 4 cm, 5 cm and 3 cm.
- Count the equal sides. The number of equal sides tells us the name.No two sides are equal.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has no equal sides: scalene.
- Look for a right angle. A triangle with a right angle is also called right-angled. The little square marks it.There is a right angle, so it is a right-angled triangle.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 0. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Tick marks show sides that are equal.Two sides have the same tick mark, so two sides are equal. The third side has no tick.
- Count the equal sides. The number of equal sides tells us the name.There are 2 equal sides.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has 2 equal sides: isosceles.
- Look for a right angle. A triangle with a right angle is also called right-angled. The little square marks it.There is a right angle, so it is a right-angled isosceles triangle.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 2. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Test each angle of the triangle with the corner of a piece of paper. The right angle fits the corner exactly.
- Look at the three angles. The little square shows where the right angle is.
- Test each angle. Acute is smaller than the paper corner. Obtuse is bigger.Angle A: right angle
Angle B: acute
Angle C: acute - Answer. The right angle is at A.
Check. A triangle can have only one right angle. ✓
Watch out. The right angle is not always at the bottom left.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. In an isosceles triangle two sides are equal, and two angles are equal. The equal angles are at the ends of the third side, opposite the equal sides.
- Find the two equal sides. The tick marks show them.Sides AB and AC are equal.
- Find the angle where the equal sides meet. This is the top of the triangle (the apex). It is on its own.The equal sides meet at A.
- Name the two equal angles. The other two angles are the same size as each other.The equal angles are at B and C.
Check. Angle B = 53° and angle C = 53° in the drawing: they are the same size. ✓
Watch out. The equal angles are not at the point where the equal sides meet.
Watch out
Do not trust the way the triangle is turned. An isosceles triangle upside down, or lying on its side, is still isosceles. Look at the sides (tick marks or lengths), not at which way the triangle points. Also, a triangle can have only one right angle.Exercise 9C Triangles
Non-calculatorKey words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Sides that have the same length are equal.The sides are 4 cm, 4 cm and 4 cm.
- Count the equal sides. The number of equal sides tells us the name.There are 3 equal sides.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has 3 equal sides: equilateral.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 3. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Sides that have the same length are equal.The sides are 7 cm, 4 cm and 7 cm.
- Count the equal sides. The number of equal sides tells us the name.There are 2 equal sides.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has 2 equal sides: isosceles.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 2. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Sides that have the same length are equal.The sides are 6 cm, 8 cm and 9 cm.
- Count the equal sides. The number of equal sides tells us the name.No two sides are equal.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has no equal sides: scalene.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 0. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Sides that have the same length are equal.The sides are 5 cm, 5 cm and 3 cm.
- Count the equal sides. The number of equal sides tells us the name.There are 2 equal sides.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has 2 equal sides: isosceles.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 2. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Tick marks show sides that are equal.All three sides have one tick mark, so all three sides are equal.
- Count the equal sides. The number of equal sides tells us the name.There are 3 equal sides.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has 3 equal sides: equilateral.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 3. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Tick marks show sides that are equal.Two sides have the same tick mark, so two sides are equal. The third side has no tick.
- Count the equal sides. The number of equal sides tells us the name.There are 2 equal sides.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has 2 equal sides: isosceles.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 2. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Tick marks show sides that are equal.Two sides have the same tick mark, so two sides are equal. The third side has no tick.
- Count the equal sides. The number of equal sides tells us the name.There are 2 equal sides.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has 2 equal sides: isosceles.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 2. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Count how many sides are equal. Three equal sides: equilateral. Two equal sides: isosceles. No equal sides: scalene. A right angle makes it right-angled too.
- Look at the three sides of the triangle. Sides that have the same length are equal.The sides are 6 cm, 5 cm and 7 cm.
- Count the equal sides. The number of equal sides tells us the name.No two sides are equal.
- Name the triangle. Three equal sides is equilateral. Two equal sides is isosceles. No equal sides is scalene.The triangle has no equal sides: scalene.
Check. Equilateral = 3 equal, isosceles = 2 equal, scalene = 0 equal. This one has 0. ✓
Watch out. Isosceles has exactly two equal sides in this book. Equilateral has all three.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. A right-angled triangle has one right angle. Test each triangle with the corner of a piece of paper.
- Test each triangle. Check every corner of every triangle with the paper corner.ABC
- Find the triangle with a right angle. The little square shows it.A: no right angle
B: has a right angle
C: no right angle - Answer. The right-angled triangle is B.
Check. The other triangles have only acute or obtuse angles. ✓
Watch out. A triangle can look right-angled without being right-angled. Test with the paper corner.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Think about what the name of the equilateral triangle tells you.
- Remember the meaning. Equilateral = 3 equal sides, isosceles = 2, scalene = none.It has 3 equal sides. All three sides are the same length.
- Write the number. The number is 3.
Check. Equilateral: 3 equal sides. ✓
Watch out. Equilateral has all 3 sides equal.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Think about what the name of the isosceles triangle tells you.
- Remember the meaning. Equilateral = 3 equal sides, isosceles = 2, scalene = none.It has 2 equal sides. The third side is different.
- Write the number. The number is 2.
Check. Isosceles: 2 equal sides. ✓
Watch out. Equilateral has all 3 sides equal.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Think about what the name of the scalene triangle tells you.
- Remember the meaning. Equilateral = 3 equal sides, isosceles = 2, scalene = none.It has no equal sides. Every side is a different length.
- Write the number. The number is 0.
Check. Scalene: 0 equal sides. ✓
Watch out. Equilateral has all 3 sides equal.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Compare the three side lengths. The sides that are the same length are the equal sides.
- Write the three lengths. Read each side from the drawing.PQ = 7 cm
QR = 5 cm
RP = 5 cm - Find which lengths match. Equal sides have the same length.QR and RP are equal.
- Name the triangle. Two equal sides is isosceles.It is isosceles.
Check. Count: 2 equal sides. ✓
Watch out. Name the triangle by its sides, not by how it is turned.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Compare the three side lengths. The sides that are the same length are the equal sides.
- Write the three lengths. Read each side from the drawing.PQ = 7 cm
QR = 5 cm
RP = 5 cm - Find which lengths match. Equal sides have the same length.QR and RP are equal.
- Name the triangle. Two equal sides is isosceles.It is isosceles.
Check. Count: 2 equal sides. ✓
Watch out. Name the triangle by its sides, not by how it is turned.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. In an isosceles triangle two sides are equal, and two angles are equal. The equal angles are at the ends of the third side, opposite the equal sides.
- Find the two equal sides. The tick marks show them.Sides AB and AC are equal.
- Find the angle where the equal sides meet. This is the top of the triangle (the apex). It is on its own.The equal sides meet at A.
- Name the two equal angles. The other two angles are the same size as each other.The equal angles are at B and C.
Check. Angle B = 53° and angle C = 53° in the drawing: they are the same size. ✓
Watch out. The equal angles are not at the point where the equal sides meet.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. In an isosceles triangle two sides are equal, and two angles are equal. The equal angles are at the ends of the third side, opposite the equal sides.
- Find the two equal sides. The tick marks show them.Sides BA and BC are equal.
- Find the angle where the equal sides meet. This is the top of the triangle (the apex). It is on its own.The equal sides meet at B.
- Name the two equal angles. The other two angles are the same size as each other.The equal angles are at A and C.
Check. Angle A = 53° and angle C = 53° in the drawing: they are the same size. ✓
Watch out. The equal angles are not at the point where the equal sides meet.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Test each angle of the triangle with the corner of a piece of paper. The right angle fits the corner exactly.
- Look at the three angles. The little square shows where the right angle is.
- Test each angle. Acute is smaller than the paper corner. Obtuse is bigger.Angle A: right angle
Angle B: acute
Angle C: acute - Answer. The right angle is at A.
Check. A triangle can have only one right angle. ✓
Watch out. The right angle is not always at the bottom left.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Look at each triangle in turn and name it by its sides. Then count the equilateral ones.
- Name each triangle. Equal sides are shown with tick marks.A: equilateral
B: isosceles
C: scalene
D: equilateral
E: isosceles
F: scalene - Pick out the equilateral triangles. A and D
- Count them. There are 2 equilateral triangles.
Check. 2 + 2 + 2 = 6 triangles in total. ✓
Watch out. An equilateral triangle has three equal sides, so we do not count it as isosceles here.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Look at each triangle in turn and name it by its sides. Then count the isosceles ones.
- Name each triangle. Equal sides are shown with tick marks.A: equilateral
B: isosceles
C: scalene
D: equilateral
E: isosceles
F: scalene - Pick out the isosceles triangles. B and E
- Count them. There are 2 isosceles triangles.
Check. 2 + 2 + 2 = 6 triangles in total. ✓
Watch out. An equilateral triangle has three equal sides, so we do not count it as isosceles here.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Look at each triangle in turn and name it by its sides. Then count the scalene ones.
- Name each triangle. Equal sides are shown with tick marks.A: equilateral
B: isosceles
C: scalene
D: equilateral
E: isosceles
F: scalene - Pick out the scalene triangles. C and F
- Count them. There are 2 scalene triangles.
Check. 2 + 2 + 2 = 6 triangles in total. ✓
Watch out. An equilateral triangle has three equal sides, so we do not count it as isosceles here.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. An equilateral triangle has 3 equal sides. The perimeter is all three sides added together. So share the perimeter equally between the 3 sides.
- Remember what equilateral means. All 3 sides are the same length.side + side + side = 24 cm
- Share the perimeter between the 3 sides. Divide by 3.24 ÷ 3 = 8
- Write the answer. Each side is the same length.Each side is 8 cm.
Check. 8 + 8 + 8 = 24. ✓
Watch out. The perimeter is the total of all the sides, not the length of one side.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Think about what each clue tells you. Two sides the same: isosceles. A right angle: right-angled.
- Use the first clue. Two equal sides is the sign of an isosceles triangle.Two equal sides: isosceles
- Use the second clue. A triangle with a right angle is right-angled.A right angle: right-angled
- Put the clues together. The triangle has both names.It is a right-angled isosceles triangle.
Check. The picture shows both the tick marks and the right-angle square. ✓
Watch out. A triangle can have more than one name.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Name each triangle. Three of them have something in common. The odd one out is the one that is different.
- Name each triangle. Tick marks show equal sides.A: isosceles
B: isosceles
C: isosceles
D: scalene - Find what three triangles share. Three are the same kind.A, B and C are isosceles (2 equal sides).
- Find the odd one out. D is scalene. It has no equal sides.
Check. Triangle D is the only one with no tick marks. ✓
Watch out. Check all four triangles before you decide.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. A triangle is a shape with 3 straight sides. That is what the word means.
- Remember what a triangle is. Tri means three.A triangle has 3 sides.
- Test with different triangles. Equilateral, isosceles, scalene and right-angled triangles all have 3 sides.Every triangle has 3 sides.
- Decide. This is always true.
Check. If a shape does not have 3 sides, it is not a triangle. ✓
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. A scalene triangle has no equal sides. Does it have a right angle? Try some.
- Try a 3, 4, 5 triangle. This triangle has no equal sides and a right angle.Scalene and right-angled. The statement is true here.
- Try 7, 5, 4. This triangle has no equal sides, but no right angle.Scalene, no right angle. The statement is not true here.
- Decide. It is true for some scalene triangles and not others.This is sometimes true.
Check. We found a scalene triangle with a right angle and one without. ✓
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. A right angle is a quarter turn. Two right angles make a straight line. See what that does to a triangle.
- Try to draw it. Put two right angles at the ends of one side.The two sides that go upwards are both at right angles to the base.
- Think about parallel lines. Two lines at right angles to the same line are parallel. They never meet.The sides can never meet to make the third corner.
- Decide. This is never true.
Check. A triangle can only have one right angle. ✓
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Join A and B to each point to make a triangle. Then look at the sides and angles of each triangle.
- Join A and B to each point. Each point gives a different triangle. Ticks show equal sides and a square shows a right angle.CDEF
- Look for isosceles triangles. Isosceles triangles have two equal sides.C is directly above the middle of AB, so AC = BC. E is 4 up from A, and AB is 4 long, so AE = AB. C and E are isosceles.
- Answer. Isosceles: C and E.
Check. Both triangles have tick marks on two sides. ✓
Watch out. Check every point. There can be more than one answer.
Key words. A triangle has 3 straight sides. Equilateral: 3 equal sides. Isosceles: 2 equal sides. Scalene: no equal sides. Right-angled: one right angle. Little tick marks show sides that are equal.
Method. Join A and B to each point to make a triangle. A right-angled triangle has a square corner.
- Join A and B to each point. The little squares show right angles.CDEF
- Look for right angles. D is directly above B, so the side BD is straight up from AB and makes a square corner. E is directly above A, so the corner at A is a right angle.D has a right angle at B. E has a right angle at A.
- Answer. Right-angled: D and E.
Check. Both D and E have a square marked. ✓
Watch out. Point E gives a triangle with a right angle and two equal sides.