Similar Triangles Triangles that have the same shape but not necessarily the same size. Corresponding angles are congruent. Meaning they have the same measure Corresponding sides are proportional. Meaning they have equal ratios Symbol for similar: ~

Corresponding Parts A B C P Q R

Example of similar triangles. Corresponding sides are proportional (ratios are equal)

Scale Factor The ratio formed by corresponding sides in similar figures is called the scale factor.

Scale Factor Example: A picture that is 8 inches tall and 10 inches wide is to be scaled to 3 inches tall to be displayed on a Web page. How wide should the picture be on the Web page for the two pictures to be similar?

Divide the height of the scaled picture by the height of the original picture to get the scale factor. Multiply the width of the original picture by the scale factor. (Scale Factor can be a ratio or a decimal number.) The picture should be 4.375 inches wide.

Finding Missing Measures Using Proportions Since corresponding sides are proportional in similar figures, you can use a proportion to find a missing measure. FIRST write the word ratio of the items being compared, then set up and solve a proportion.

Example 1 The missing length is 3 3/8 cm. Word ratio: Proportion: x cm 9 cm The missing length is 3 3/8 cm.

EX: Find the length of side y. A B C X Y 36 m y 3m 18 m

EX: Find the length of side y. A B C X Y 36 m y 3m The missing side is 6 cm. 18 m