Page 87 - MAT KS3 Y8 Cambridge CheckPoint

8.1 Recognising congruent shapes

✦ Exercise 8.1

1 Which side is the hypotenuse in each right-angled triangle?
a b c d
A I
L
D E H

B C K M
F J
2 Which of these shapes are congruent to shape A?

A B C D E F G

3 These two triangles are congruent.
U X
6.5 cm 95° 3.1 cm
62° 23°
V W Y Z
7.8 cm
a Write down the length of the side: i UW ii XZ iii YZ.
b Write down the size of: i ∠UVW ii ∠UWV iii ∠YXZ
4 These two shapes are drawn accurately.
B E
They are congruent.
A F

D C H G
a Which side corresponds to: i AD ii BC iii EF iv GH?
b Which angle corresponds to: i ∠ADC ii ∠BAD iii ∠FEH iv ∠EHG?

5 This is part of Razi’s homework.

Question Here are two accurately drawn
congruent shapes.
a Write down one pair of
corresponding angles.
b Explain why these angles are
corresponding.
Answer a ∠LKN and ∠SRQ are corresponding.
b They are corresponding because they are both 90°.

Has Razi got his homework correct? Explain your answer.
6 Read what Harsha says. Is she correct? Explain your answer.

In an equilateral triangle all the angles are 60°. This means that all equilateral
triangles must be congruent as all the angles are the same size.

8 Shapes and geometric reasoning 85