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Geometry Lesson 6: Similar Triangles and Proportional Sides

Learn how to determine if two triangles are similar and find missing measures of similar triangles through proportional relationships of corresponding sides. Practice calculating heights and shadows in real-world scenarios.

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Geometry Lesson 6: Similar Triangles and Proportional Sides

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  1. (over Lesson 10-5) Find the distance between the points. Express answers in simplest radical form and as decimal approximations rounded to the nearest hundredth, if necessary. • A • B • C • D (9,2) and (3,10) 10 (–2, –4) and (3, 8) 13 (–5, 0) and (1, –7) Find the possible values of a if (9, –12) and (2, a) are 25 units apart. –36 or 12 5Min 6-1

  2. Determine whether two triangles are similar. • Find the unknown measures of sides of two similar triangles. • similar triangles Lesson 6 MI/Vocab

  3. Animation: Similar Triangles Key Concept 10-6a

  4. Determine Whether Two Triangles Are Similar Determine whether the pair of triangles is similar. Justify your answer. Lesson 6 Ex1

  5. Determine Whether Two Triangles Are Similar Answer: The corresponding sides of the triangles are proportional, so the triangles are similar. Lesson 6 Ex1

  6. Determine whether the pair of triangles is similar. • A • B • C A. The triangles are similar. B. The triangles are not similar. C. cannot be determined Lesson 6 CYP1

  7. Find Missing Measures A. Find the missing measures if the pair of triangles is similar. Corresponding sides of similar triangles are proportional. Lesson 6 Ex2

  8. Find Missing Measures CE = 8, GI = y, ED = 18, and GH = 27 216 = 18y Find the cross products. 12 = y Divide each side by 18. Corresponding sides of similar triangles are proportional. CD = 18, GH = 27, ED = 18, and IH = x 18x = 486 Find the cross products. x = 27 Divide each side by 18. Answer: The missing measures are 27 and 12. Lesson 6 Ex2

  9. B. Find the missing measure if the pair of triangles is similar. Find Missing Measures Corresponding sides of similar triangles are proportional. XY = 4, XZ = 10, XW = 3, and XV = a. 4a = 30 Find the cross products. Lesson 6 Ex2

  10. Find Missing Measures a = 7.5 Divide each side by 4. Answer: The missing measure is 7.5. Lesson 6 Ex2

  11. A. Find the missing measures if the pair of triangles is similar. • A • B • C • D A. 14 and 28 B. 6 and 42 C. 18 and 28 D. 18 and 42 Lesson 6 CYP2

  12. B. Find the missing measure if • A • B • C • D A. 5.25 B. 6 C. 16 D. 14 Lesson 6 CYP2

  13. SHADOWSRichard is standing next to the General Sherman Giant Sequoia tree in Sequoia National Park. The shadow of the tree is 22.5 meters, and Richard’s shadow is 53.6 centimeters. If Richard’s height is 2 meters, how tall is the tree? Since the length of the shadow of the tree and Richard’s height are given in meters, convert the length of Richard’s shadow to meters. Lesson 6 Ex3

  14. Richard’s shadow Richard’s height Tree’s shadow Tree’s height 1 m = 100 cm = 0.536 m Simplify. Let x = the height of the tree. 0.536x = 45 Cross products x≈ 83.96 Answer: The tree is about 84 meters tall. Lesson 6 Ex3

  15. TOURISM Trudie is standing next to the Eiffel Tower in France. The height of the Eiffel Tower is 317 meters and casts a shadow of 155 meters. If Trudie’s height is 2 meters, how long is her shadow? • A • B • C • D A. 2 m B. 0.98 m C. 3.2 m D. 1.45 m Lesson 6 CYP3

  16. Chapter 10 Lesson 6 homework: Worksheet page 46

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