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
Similar Triangles
Similarity and Congruence
Similar triangles – all angles are the same, sides of different lengths but in
constant ratio
E
B
A
C
F
D
Triangles ABC and DEF are similar because:
Bˆ  Eˆ
Aˆ  Dˆ
Cˆ  Fˆ
by subtraction
Ratio of sides =
DF = EF
AC
BC
Similar Triangles
Similarity and Congruence
Triangles ABC and DEF are similar
Find
i) AC
ii) DE
E
B
y
4
A
9
6
x
C
D
5
F
Similar Triangles
Similarity and Congruence
P
Find x
1.5
X
4.5
R
3
Y
x
Q
Similarity and Congruence
1)
Comparing Areas &
Volumes of Similar Shapes
2m
1m
x
2)
5
32cm2
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.
50cm2
The above two rectangles are similar.
Find x.
Similarity and Congruence
3)
Comparing Areas &
Volumes of Similar Shapes
The sides of two cubes are in the ratio 2 : 5
i) Write down the ratio of their area
ii) Write down the ratio of their volume
iii) Find the volume of the larger if the volume of the smaller cube is 10cm3
Summary
Length Ratio
Area Ratio
Volume Ratio
a:b
a2 : b2
a3: b3
Similarity and Congruence
Additional Notes
Similarity and
Congruence
Learning Outcomes:
At the end of the topic I will be able to

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
Can
Do
Revise
Further
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