congruence and similarity. similar two shapes are similar if their corresponding angles are equal...

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.