(8) Lesson 7.5 - Similar Triangles and Indirect measurement
- 1. Course 3, Lesson 7-5 1. Determine whether the pair of polygons is similar. Explain. 2. The pair of polygons is similar. Determine the missing side measure. 3. A greeting card is 8 inches by 6 inches, but it will have to be cut to fit in an envelope. The scale factor from the original card to the smaller card is 5:4. Determine the dimensions of the smaller card.
- 2. Course 3, Lesson 7-5 ANSWERS 1. No; corresponding sides are not proportional. 2. 3. × 3 ; 4.5 4 6 x x 2 6 5 4 4 5
- 3. HOW can you determine congruence and similarity? Geometry Course 3, Lesson 7-5
- 4. Course 3, Lesson 7-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. • 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. 7 Look for and make use of structure. Geometry
- 5. To • write similarity statements for similar triangles, • use indirect measurement to find missing measures on a right triangle Course 3, Lesson 7-5 Geometry
- 6. • indirect measurement Course 3, Lesson 7-5 Geometry
- 7. Course 3, Lesson 7-5 Geometry Words If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Symbols If Model , , .A F B G ABC FGH and then
- 8. 1 Need Another Example? Step-by-Step Example 1. Determine whether the triangles are similar. If so, write a similarity statement. Angle A and ∠E have the same measure, so they are congruent. Since 180 – 62 – 48 = 70, ∠G measures 70°. Two angles of EFG are congruent to two angles of ABC, so ABC ~ EFG.
- 9. Answer Need Another Example? Determine whether the triangles are similar. If so, write a similarity statement. The triangles are not similar.
- 10. 1 Need Another Example? 2 3 4 Step-by-Step Example 2. A fire hydrant 2.5 feet high casts a 5-foot shadow. How tall is a street light that casts a 26-foot shadow at the same time? Let h represent the height of the street light. Shadow Height hydrant hydrant street light street light = 5 2.5 h26 5h = 26 • 2.5 5h = 65 Find the cross products. Multiply. Divide each side by 5. The street light is 13 feet tall. h = 13
- 11. Answer Need Another Example? How tall is the flagpole? 38.5 ft
- 12. 1 Need Another Example? 2 3 4 5 6 Step-by-Step Example 3. In the figure at the right, triangle DBA is similar to triangle ECA. Ramon wants to know the distance across the lake. 320d = 482 • 40 d = 60.25 AB corresponds to AC and BD corresponds to CE. Find the cross products. The distance across the lake is 60.25 meters. Replace AB with 320, AC with 482, and BD with 40. Multiply. Then divide each side by 320.
- 13. Answer Need Another Example? The two triangles in the figure are similar. Find the distance across the lake. 15 m
- 14. How did what you learned today help you answer the HOW can you determine congruence and similarity? Course 3, Lesson 7-5 Geometry
- 15. How did what you learned today help you answer the HOW can you determine congruence and similarity? Course 3, Lesson 7-5 Geometry Sample answer: • In triangles, if two angles of one triangle are congruent to two angles of another triangle, the two triangles are similar.
- 16. How did yesterday’s lesson about similar triangles help you to learn about angle-angle-similarity? Course 3, Lesson 7-5 Ratios and Proportional RelationshipsFunctionsGeometry