2. Introduction
Recognizing and using congruent and similar shapes can make calculations and design work easier. For instance, in the design at the corner, only two different shapes were actually drawn. The design was put together by copying and manipulating these shapes to produce versions of them of different sizes and in different positions.

3. Similar and Congruent Figures
Congruent triangles have all sides congruent and all angles congruent.
Similar triangles have the same shape; they may or may not have the same size.

4. Similar and Congruent Figures
Note: Two figures can be similar but not congruent, but they can’t be congruent but not similar. Think about why!

5. Examples
These figures are similar and congruent. They’re the same shape and size.
Symbolized by ≅

6. Ratios and Similar Figures
Similar figures have corresponding sides and corresponding angles that are located at the same place on the figures.
Corresponding sides have to have the same ratios between the two figures.
A ratio is a comparison between 2 numbers (usually shown as a fraction)

7. Ratios and Similar FiguresB E F
Example G H C D
These angles correspond:
A and E
B and F
D and H
C and G
These sides correspond:
AB and EF
BD and FH
CD and GH
AC and EG

8. Ratios and Similar Figures
Example
These rectangles are similar, because the ratios of these corresponding sides are equal:

9. Proportions and Similar Figures
A proportion is an equation that states that two ratios are equal.
Examples:
n = m = 4

10. Proportions and Similar Figures
You can use proportions of corresponding sides to figure out unknown lengths of sides of polygons.
16 m
10 m n
5 m

11. Proportions and Similar Figures
You can use proportions of corresponding sides to figure out unknown lengths of sides of polygons.
16 m
10 m n
5 m

12. Similar triangles Similar triangles are triangles with the same shape
For two similar triangles,
corresponding angles have the same measure
length of corresponding sides have the same ratio
65o
25o A
4 cm
2cm
12cm B
Example
Angle A = 90o
Side B = 6 cm

13. Proportions and Similar Figures
Can you solve for the missing variable in these similar triangles? 12 J 20 12

14. PRACTICE PROBLEMS Ratio and proportion review Page 581 #1, 2, 6-13
Similar polygon problems Page 591 #12-19