Ratios and Proportions Geometry Unit 11, Day 1 Ms. Reed

Review: Solve for x 1. 4 = 24 x 54 2. 12 = x 16 8

Similar Figures Figures are similar if Corresponding angles are congruent Corresponding sides are proportional The ratio of the corresponding sides is called the similarity ratio

Find the Similarity Ratio: B C D E F AB = BC = AC = DE EF DF We can now say ΔABC ~ ΔDEF The similarity ratio is 1/2 Similarity Statement

ΔXYZ ~ ΔMNP with a similarity ratio of 1/3 Example: Write a similarity statement and give the similarity ratio of the following: 42 P N Y 14 48 12 36 X Z 16 M ΔXYZ ~ ΔMNP with a similarity ratio of 1/3

Proportions Proportion – a statement of two equal ratios a = c OR a : b = c : d b d

Extended Proportion An extended proportion can be written when 3 or more ratios are equal. 18 = 15 = 12 24 20 16

Are the polygons similar? #1 If the polygons are similar write a similarity statement and give the similarity ratio. E F 30 H G A B 20 D C 36 52 NOT SIMILAR

Are the polygons similar? #2 21 W X Y Z A B C D 14 6 6 4 4 9 6 ABCD ~ WXYZ with a similarity ratio of 2/3

Leaning Tower of Pisa The Leaning Tower of Pisa in Italy is about 180 ft tall. A souvenir paperweight of the Leaning Tower is 6 in. tall. What is the similarity ratio of the paperweight to the real tower?

Practice Find the value of all the variables if ΔABC ~ ΔDEF w = 21 x = 101° y = 27° z = 12 B E z 8 x° 9 6 27° 52° y° A D F C w 28