Anglesin a Triangle (2)

𝟒𝟎°

?

?

Write down somepossible values

𝟒𝟎°

70°

70°

Did anyone write downthis option?

𝟒𝟎°

70° 70°

What type of triangledo we have here?

Isosceles triangle

What do you notice about the angles and the sides?

FACTS

Isosceles triangles

Remember… triangles can come in all different shapes and sizes but the same rules apply!

The word “isosceles” means ‘equal legs’.

What do you have at the bottom of equal legs?

Activity 2 Angles in a Triangle (2)

How can we use the use the hatch marks to identify the equal angles?

Calculate the missing angles in the isosceles

triangles.

65

b

a

50

d

e f g

35

Activity 2 Angles in a Triangle (2)

Calculate the missing angles in the isosceles

triangles.

65

b

a

50

d

e f g

35

a = 65

b = 50

e = 65

d = 65

f = 72.5

g = 72.5

Calculating Angles 2

Calculate the size of angle of 𝑏.Example1:

Angles in a triangle add to 180°

180° – 80° = 1002𝑏 = 100°𝑏 = 100° ÷ 2𝑏 = 50°

Base angles ofan isoscelestriangle are equal

80°

𝑏 𝒃

FACTS

Equilateral triangles

All angles are equal and all sides are equal in length

Activity 2 Angles in a Triangle (2)

What type of triangle is

this?

What will the size of each

angle be?

How do you know?

Will this always be the

same for this type of

triangle?

Explain your answer.

Activity 2 Angles in a Triangle (2)

What type of triangle is

this?

What will the size of each

angle be?

How do you know?

Will this always be the

same for this type of

triangle?

Explain your answer.

Equilateral triangle. Equilateral

triangle have the same angle

size.

FACTS

Scalene triangles

All sides are different lengths and all angles are different

FACTS

Right-angled triangles

One 90° angle and two angles that add to 90°

Angles in a Triangle (2)Reasoning - 1

I have an isosceles triangle. One angle measures 44

degrees. What could the other angles measure?

44

Angles in a Triangle (2)Reasoning - 1

I have an isosceles triangle. One angle measures 44

degrees. What could the other angles measure?

44 The angles could be:

92° or 68°, 68°

Calculate the angle of 𝑎.Example 2:

Angles in a triangle add to 180°There are 360° in a full turn at a point

𝑏 = 180° – 138°𝑏 = 42°c = 180° − 65° − 42°𝑐 = 73°

Can these angles help you?

𝒃

𝒄

𝑎 = 360° − 73°𝑎 = 287°

Angles in a Triangle (2)Reasoning - 2

What type of triangle is each person describing?

Explain how you know.

My angles are

70°, 70° and

40°

My angles are

45°, 45° and

90°

My angles are

60°, 60°and

60°

Esin Malachi Tia

19

Angles in a Triangle (2)Reasoning - 2

6 - Properties of

Shape

What type of triangle is each person describing?

Explain how you know.

My angles are

70°, 70° and

40°

My angles are

45°, 45° and

90°

My angles are

60°, 60°and

60°

Esin Malachi Tia

Esin is describing

an isosceles

triangle.

Malachi is

describing an

isosceles right-

angled triangle.

Tia is describing

an equilateral

triangle.

Angles in a Triangle (2)Reasoning - 2

How many sentences can you write to express the

relationships between the angles in the triangles?

One has been done for you.

40

a d

40° + a + b = 180°

b c

Angles in a Triangle (2)Reasoning - 2

How many sentences can you write to express the

relationships between the angles in the triangles?

One has been done for you.

40

a d

40° + a + b = 180°

b c

Possible responses:

20° + a + b = 180°

20° + c + d = 180°

b = 90 °

c = 90 °

b = c

a = d

etc. Children could also work

out the value of each

angle.

CHALLENGE!!! Consider this. . . . .

𝑨𝑩𝑪𝑫 is a square. 𝑷 and 𝑸 are points outside the square such that triangles 𝑨𝑩𝑷 and 𝑩𝑪𝑸 are

both equilateral. How big is angle ∠𝑷𝑸𝑩?

𝐴

𝐵 𝐶

𝐷

𝑄

𝑃

60°

60°90°

Discussion Angles in a Triangle (2)

How can we identify sides which are the same length on a

triangle?

How can we use the use the hatch marks to identify the

equal angles?

If you know one angle in an isosceles triangle, what else do

you know?

Can you have an isosceles right-angled triangle?