Similarity and Congruence

Learning Outcomes

Know when shapes are similar

Know when shapes are congruent

Use similarity to find the missing sides of 2-D shapes

Use congruency to find the missing sides of triangles

Compare areas and volumes of similar shapes

Similarity and Congruence Similar Triangles

Similar triangles – all angles are the same, sides of different lengths but in constant ratio

Triangles ABC and DEF are similar because:

FC

DA

EB

ˆˆˆˆˆˆ

by subtraction

Ratio of sides = DF = EF AC BC

A

B

C D

E

F

Similarity and Congruence Similar Triangles

Triangles ABC and DEF are similarFind i) AC

ii) DE

A

B

C D

E

F

4 6

x 5

9y

Similarity and Congruence Similar Triangles

Find x

R

X

P

QY

4.5

1.5

x3

Similarity and CongruenceComparing Areas &

Volumes of Similar Shapes

1)

1m2m

The above two rectangles are similar.

i) If the above area of the smaller rectangle is 20m2 find the area of the larger rectangle.

ii) If the area of the larger is 40m2, find the area of the smaller.

2)

5

x

The above two rectangles are similar. Find x.

50cm232cm2

Similarity and CongruenceComparing Areas &

Volumes of Similar Shapes

3) The sides of two cubes are in the ratio 2 : 5

i) Write down the ratio of their areaii) Write down the ratio of their volumeiii) Find the volume of the larger if the volume of the smaller cube is 10cm3

Summary

Length Ratio a : b

Area Ratio a2 : b2

Volume Ratio a3: b3

Similarity and Congruence Additional Notes

Similarity and Congruence

Learning Outcomes:At the end of the topic I will be able to

Can Revise Do Further

Know when shapes are similar

Know when shapes are congruent

Use similarity to find the missing sides of 2-D shapes

Use congruency to find the missing sides of triangles

Compare areas and volumes of similar shapes