Pearson Unit 3 Topic 9: Similarity 9-1: Similar Polygons Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

TEKS Focus: (7)(B) Apply the Angle-Angle criterion to verify similar triangles and apply the proportionality of the corresponding sides to solve problems. (1)(A) Apply mathematics to problems arising in everyday life, society, and the workplace. (1)(F) Analyze mathematical relationships to connect and communicate mathematical ideas. (1)(G) Display, explain, or justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

A figure with the same SHAPE but not necessarily the same SIZE VOCABULARY: Vocabulary Word Definition Similar Figure A figure with the same SHAPE but not necessarily the same SIZE Scale Factor The RATIO of corresponding linear measurements in similar figures Proportion An equation that states 2 ratios are equal

If the scale factor of a dilation is greater than 1 (k > 1), it is an enlargement. The scale factor in fraction form is an improper fraction. If the scale factor is less than 1 (k < 1), it is a reduction. The scale factor in fraction form is a proper fraction. Helpful Hint 0 < k < 1,

Example 1:

Example 2: Compare short/short and long/long. 10 = 15 15 20 10 = 15 15 20 Rectangle KLMN ~ Rectangle XYZW 18 = 18 = 18 = 12 = 12 9 9 9 6 6 All ratios = 2. Pentagon ABCDE ~ Pentagon RSTUV

Example 3: 6 = y 9 5 9y = 30 y = 3 1/3

Example: 4

Example: 5 Length of main span in scale drawing is 6.4 cm.

Example: 6 1 = x 50 605 50x = 605 x = 12.1 in No, the paper would need to be over 12 inches tall