1. Congruence and Similarity

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

3. Bottom Length 10 cm Top Length 3 cm

4. Congruent
Two shapes are congruent if all corresponding angles AND sides are equal.
If two shapes are congruent, they are also similar.

5. Top Length 4 cm
Bottom Length 5 cm

6. Perimeter
To find the perimeter of any polygon, add up the length of all sides.

7. 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.

8. 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.

9. Scale Factor
The ratio of corresponding side lengths of two similar figures.
All congruent shapes have a scale factor of 1:1.

10. 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

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

12. 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. = x
So, x = 1 cm B
Length = 4 cm
Width = ? cm

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

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