Congruence and Similarity

Similar Two shapes are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Bottom Length 10 cm Top Length 3 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.

B A The scale factor from A to B is 5:2. Length = 10 cm Width = 5 cm The scale factor from A to B is 5:2. The ratio of areas from A to B is 25:4 Length = 4 cm Width = 2 cm B

Missing Side You can find the missing side length on one of two similar figures by using a proportion involving scale factor.

B A Set up a proportion. Cross multiply and divide. 20 = 5 4 x A and B are similar. A Length = 20 cm Width = 5 cm Set up a proportion. Cross multiply and divide. 20 = 5 4 x So, x = 1 cm B Length = 4 cm Width = ? cm

Missing Angle You can find the measure of a missing angle on one of two similar triangles by subtracting from 180 degrees.

If triangles xyz and def are similar, what is the measure of angle y? 500 y z d Y = 60 degrees because 50 + 70 = 120. 180 – 120 = 60. e f 700