Geometry Lesson 7.3.notebook March 11, 2015

Bell Ringer Due after attendance

a. Determine if the two parallelograms are similar. If so, write the similarity statement. If not, explain your reasoning.

b. On a map of Colorado, the cities of Colorado Springs and Denver are 10.5 inches apart. If the scale on the map states that 1.5 inches equals 10 miles, find the actual distance from Colorado Springs to Denver.

1 Geometry Lesson 7.3.notebook March 11, 2015

a. ABCD PRSQ

b.

2 Geometry Lesson 7.3.notebook March 11, 2015

SIMILAR TRIANGLES In Chapter 4, we learned tests for congruent triangles. They were SSS, SAS, ASA, and AAS.

In this section, we will learn ways to test for similar triangles.

Angle­Angle (AA) Similarity Postulate ­ If two angles of one triangle are congruent to two angles of a second triangle, then the triangles are similar.

Determine whether the triangles are similar. If so, write the similarity statement.

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Side­Side­Side (SSS) Similarity Theorem ­ If the corresponding side lengths of two triangles are proportional, then the triangles are similar.

Side­Angle­Side (SAS) Similarity Theorem ­ If the lengths of two sides of one triangle are proportional to the lengths of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar.

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Working with a partner, determine if the triangles are similar. If similar, write a similarity statement. Explain your reasoning.

a. b.

c. d.

Properties of Similarity Reflexive Property Symmetric Property Transitive Property

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Parts of Similar Triangles

Find BE and AD.

Because then

by corresponding angles. So,

On your own, find QP and MP. Compare your answer with those around you.

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A. Hallie is estimating the height of the Superman roller coaster in Mitchellville, Maryland. She is 5 feet 3 inches tall and her shadow is 3 feet. If the length of the shadow of the roller coaster is 40 feet, how tall is the roller coaster?

First, we must get all measurements into the same units. becomes 5.25 ft. Now set up the proportion.

Coaster is 70 ft. tall.

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B. Adam is standing next to the Palmetto Building in Columbus, South Carolina. He is 6 feet tall and the length of his shadow is 9 feet. If the length of the shadow of the building is 322.5 feet, how tall is the building?

1. Working with a neighbor set up the proportion that will be used to solve this problem.

2. Find the height of the Palmetto Building. Compare with others around you.

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P. 479 9­23 (you may work in groups until the bell)

9