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.

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.

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!

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

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)

Ratios and Similar Figures B 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

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

Proportions and Similar Figures A proportion is an equation that states that two ratios are equal. Examples: n = 5 m = 4

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  

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  

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

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

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