Chapter 10 Geometry Do Now l Complete numbers

Chapter 10 Geometry

Do Now l Complete numbers 8 – 14 on page 430

Chapter 10 Lesson 6 Similar Figures Objective: Determine whether figures are similar and find a missing length in a pair of similar figures.

Geometry The study of properties, measurement, and relationships of points, angles, surfaces and solids.

Similar Figures that have the same shape but not necessarily the same size. Corresponding sides are proportional Corresponding angles are congruent

Congruent Equal ~ =

A D E B AB C EF F Write each fraction in simplest form. H G 1. AB 3 EF 9 2. BC 1 = FG 3 = 1 3

Indirect measurement Finding measurement by using similar triangles and writing a proportion

A D B ABC ~ F E C DEF Corresponding sides: AB DE Corresponding angles: = AC DF A ~ = = BC EF D; ~ B = E; C ~ = F

A D 6 m 5 m 18 m 15 m B C E F 4 m If ABC ~ DEF, find the length of EF Write a proportion AC DF = BC EF 6 = 18 4 n N=12

Kelly wants to resize a 4 -inch wide by 5 -inch long photo. It is to fit in a space that is 2 inches wide. What is the length of the resized photo in inches? X 5 in. 2 in. 4 in.

Find the value of x in each pair of similar figures. A D 5 mi 6 mi 30 mi X B C E F

Find the value of x in each pair of similar figures. A D 29. 4 m B 14 m C 25. 2 m E X F

A B E F X 14 cm G C 31. 5 cm D 9 cm H

Determine whether each pair of figures is similar. Justify your answer. A B 6 in E F 18 in G C D 11 in H 33 in

Determine whether each pair of figures is similar. Justify your answer. A D 21 km B 54 km E 18 km 63 km

If ABC DEF, find the length of

Since the two triangles are similar, the ratios of their corresponding sides are equal. So, you can write and solve a proportion to find Write a proportion. Let n represent the length of Then substitute. Find the cross products. Simplify. Divide each side by 3. Answer: The length of is 16. 5 centimeters. .

If JKL MNO, find the length of Answer: 13. 5 in.

GRID-IN TEST ITEM A rectangular picture window 12 -feet long and 6 -feet wide needs to be shortened to 9 feet in length to fit a redesigned wall. If the architect wants the new window to be similar to the old window, how wide will the new window be? Read the Test Item To find the width of the new window, draw a picture and write a proportion.

Solve the Test Item Write a proportion. Find the cross products. Divide each side by 12.

So, the width of the new window will be 4. 5 feet. Answer: 4. 5 feet

GRID-IN TEST ITEM Tom has a rectangular garden which has a length of 12 feet and a width of 8 feet. He wishes to start a second garden which is similar to the first and will have a width of 6 feet. Find the length of the new garden. Answer: 9

Kelly bought a miniature replica of the Statue of Liberty. The replica is 9 inches tall, and the length of the statue’s right arm holding the torch is 1 ¼ inches. 1. About how long is the State of Liberty’s right arm? 2. Kelly’s friend Bella brought home a smaller replica. The length of the Statue’s right arm is ¾ inch. How tall is Bella’s statue?