We will determine1 how to use the Proportional2 Relationships to find the missing segment lengths. LEARNING OBJECTIVE Definition figure out Two ratios that have the same value. Declare the Objective A: Read the Objective to B. B: Define Proportionality to A. CFU What are we going to learn today? What is “Proportionality” mean? G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

ACTIVATE PRIOR KNOWLEDGE Remember the Concept Cross Products property. Write the correct proportion that could be use to find the height? 1. 2. Write two other proportions ACTIVATE PRIOR KNOWLEDGE Make the Connection Students, you already know how to write the correct proportion. Today, we will learn how to use the Proportional Relationships to find the missing segment lengths.

Remember the Concept For example, on a map with a scale of 1 cm : 1500 m, one centimeter on the map represents 1500 m in actual distance. A scale drawing represents an object as smaller than or larger than its actual size. The drawing’s scale is the ratio of any length in the drawing to the corresponding actual length. Helpful Hint A proportion may compare measurements that have different units. Whenever dimensions are given in both feet and inches, you must convert them to either feet or inches before doing any calculations. Remember the Concept 1 feet = 12 inches On your white board, convert the feet into inches: 5 feet 6 in. and 15.5 ft CFU Check for Understanding A Explain to B: What is scale drawing & AA Similarity? 5(12) + 6 in. = 66 inches 15(12) + 6 in = 186 inches

Check for Understanding B Explain to A: What is proportional Perimeters and Areas Theorem?

Check for Understanding How did I/you write the proportional ratios? How did I/you I solve for x? CFU 1 2 Write the ratio using Triangle Proportionality theorem. Use the Cross Product rule to solve for x. Check you answer. Steps to find the segment lengths 1 2 3 1. A student wanted to find the height h of a statue of a pineapple in Nambour, Australia. She measured the pineapple's shadow and her own shadow. The student's height is 5 feet 8 inches. What is the height of the pineapple? Round to the nearest tenth if necessary. First, we need the same units, so convert the feet into inches. 5 ft 8 in = 68 in., 2 ft = 24 in., and 8 ft 9 in. = 105 in. CONCEPT DEVELOPMENT Check for Understanding A Explain to B: How did I write the ratio and solve for h?

How did I/you write the proportional ratios? How did I/you I solve for x? CFU 1 2 Write the ratio using Triangle Proportionality theorem. Use the Cross Product rule to solve for x. Check you answer. Steps to find the segment lengths 1 2 3 1. 2. Jenny is 5 feet 6 inches tall. To find the height h of a light pole, she measured her shadow and the pole's shadow. What is the height of the pole? Give the height as a mixed number (a whole number and a fraction). CONCEPT DEVELOPMENT ℎ 186 = 66 93 2 186 186 The pole is 11 feet tall.

To find the height h of a dinosaur in a museum, How did I/you write the proportional ratios? How did I/you I solve for x? CFU 1 2 Write the ratio using Triangle Proportionality theorem. Use the Cross Product rule to solve for x. Check you answer. Steps to find the segment lengths 1 2 3 To find the height h of a dinosaur in a museum, Amir placed a mirror on the ground 40 feet from its base. Then he stepped back 4 feet so that he could see the top of the dinosaur in the mirror. Amir's eyes were approximately 5 feet 4 inches above the ground. What is the height of the dinosaur? 1. Liam is 6 feet tall. To find the height of a tree, he measures his shadow and the tree's shadow. The measurements of the two shadows are shown. Find the height h of the tree. Round to the nearest tenth if necessary. 2. CONCEPT DEVELOPMENT

1. In order to find the height of a cliff, you stand How did I/you write the proportional ratios? How did I/you I solve for x? CFU 1 2 Write the ratio using Triangle Proportionality theorem. Use the Cross Product rule to solve for x. Check you answer. Steps to find the segment lengths 1 2 3 1. In order to find the height of a cliff, you stand at the bottom of the cliff: Find JK: 2. Find the height x of a flagpole CONCEPT DEVELOPMENT

Relevance Reason #1: Proportional Relationships are used in finding the Distance To find the distance d across a stream, Mario located points as shown in the figure. Use the given information to find d . Round your answer to the nearest tenth if necessary. Relevance Reason #2: Know how to find geometric mean will help you do well on tests (PSAT, SAT, ACT, GRE, GMAT, LSAT, etc..). Check for Understanding Does anyone else have another reason why it is relevant to use Proportional Relationships? Which reason is most relevant to you? Why?

What did you learn today about how to use the Proportional Relationships to find the missing segment lengths. Word Bank Proportional Segment Lengths Scale Drawing AA Similarity Postulate Similar Triangles SUMMARY CLOSURE Today, I learned how to __________________ ______________________________________________________________.