Congruence and Similarity

Similar• Two shapes are similar if

their corresponding angles are equal and their corresponding sides are in proportion.

Top Length 5 cm

Bottom Length 10 cm Top Length 3 cm

Bottom Length 6 cm

600 600

1200 1200

Congruent • Two shapes are congruent if

all corresponding angles AND sides are equal. • If two shapes are congruent,

they are also similar.

Top Length 4 cm

110 0 110 0

70 0 70 0

Bottom Length 5 cm

Perimeter• To find the perimeter of

any polygon, add up the length of all sides.

Triangles• Triangles have 3 angles that

add up to 180 degrees.• To find the area of a

triangle, multiply ½ the base x the height.

Rectangles•Rectangles have 4 right

angles that add up to 360 degrees.• To find the area of a

rectangle, multiply the length x the width.

Scale Factor• The ratio of corresponding

side lengths of two similar figures.•All congruent shapes have

a scale factor of 1:1.

ALength = 10 cm

Width = 5 cm

Length = 4 cm

Width = 2 cm

The scale factor from A to B is 5:2.The ratio of areas from A to B is 25:4

B

Missing Side• You can find the missing

side length on one of two similar figures by using a proportion involving scale factor.

ALength = 20 cm

Width = 5 cm

Length = 4 cm

Width = ? cm

Set up a proportion. Cross multiply and divide.20 = 54 xSo, x = 1 cm B

A and B are similar.

Missing Angle• You can find the measure

of a missing angle on one of two similar triangles by subtracting from 180 degrees.

500

700

y z

x

d

e f

If triangles xyz and def are similar, what is the measure of angle y?

Y = 60 degrees because 50 + 70 = 120.180 – 120 = 60.