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# Geometry Section 4-6 1112

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Isosceles and Equilater

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### Geometry Section 4-6 1112

1. 1. Section 4-6 Isosceles and Equilateral TrianglesWednesday, February 8, 2012
2. 2. Essential Questions ❖ How do you use properties of isosceles triangles? ❖ How do you use properties of equilateral triangles?Wednesday, February 8, 2012
3. 3. Vocabulary 1. Legs of an Isosceles Triangle: 2. Vertex Angle: 3. Base Angles:Wednesday, February 8, 2012
4. 4. Vocabulary 1. Legs of an Isosceles Triangle: The two congruent sides of an isosceles triangle 2. Vertex Angle: 3. Base Angles:Wednesday, February 8, 2012
5. 5. Vocabulary 1. Legs of an Isosceles Triangle: The two congruent sides of an isosceles triangle 2. Vertex Angle: The included angle between the legs of an isosceles triangle 3. Base Angles:Wednesday, February 8, 2012
6. 6. Vocabulary 1. Legs of an Isosceles Triangle: The two congruent sides of an isosceles triangle 2. Vertex Angle: The included angle between the legs of an isosceles triangle 3. Base Angles: The angles formed between each leg and the base of an isosceles triangleWednesday, February 8, 2012
7. 7. Theorems and Corollaries Theorem 4.10 - Isosceles Triangle Theorem: Theorem 4.11 - Converse of Isosceles Triangle Theorem: Corollary 4.3 - Equilateral Triangles: Corollary 4.4 - Equilateral Triangles:Wednesday, February 8, 2012
8. 8. Theorems and Corollaries Theorem 4.10 - Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent Theorem 4.11 - Converse of Isosceles Triangle Theorem: Corollary 4.3 - Equilateral Triangles: Corollary 4.4 - Equilateral Triangles:Wednesday, February 8, 2012
9. 9. Theorems and Corollaries Theorem 4.10 - Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent Theorem 4.11 - Converse of Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Corollary 4.3 - Equilateral Triangles: Corollary 4.4 - Equilateral Triangles:Wednesday, February 8, 2012
10. 10. Theorems and Corollaries Theorem 4.10 - Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent Theorem 4.11 - Converse of Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Corollary 4.3 - Equilateral Triangles: A triangle is equilateral IFF it is equiangular Corollary 4.4 - Equilateral Triangles:Wednesday, February 8, 2012
11. 11. Theorems and Corollaries Theorem 4.10 - Isosceles Triangle Theorem: If two sides of a triangle are congruent, then the angles opposite those sides are congruent Theorem 4.11 - Converse of Isosceles Triangle Theorem: If two angles of a triangle are congruent, then the sides opposite those angles are congruent. Corollary 4.3 - Equilateral Triangles: A triangle is equilateral IFF it is equiangular Corollary 4.4 - Equilateral Triangles: Each angle of an equilateral triangle measures 60°Wednesday, February 8, 2012
12. 12. Example 1 a. Name two unmarked congruent angles. b. Name two unmarked congruent segmentsWednesday, February 8, 2012
13. 13. Example 1 a. Name two unmarked congruent angles. b. Name two unmarked congruent segmentsWednesday, February 8, 2012
14. 14. Example 1 a. Name two unmarked congruent angles. b. Name two unmarked congruent segmentsWednesday, February 8, 2012
15. 15. Example 2 Find each measure. a. b. PRWednesday, February 8, 2012
16. 16. Example 2 Find each measure. a. 180 - 60 b. PRWednesday, February 8, 2012
17. 17. Example 2 Find each measure. a. 180 - 60 = 120 b. PRWednesday, February 8, 2012
18. 18. Example 2 Find each measure. a. 180 - 60 = 120 120 ÷ 2 b. PRWednesday, February 8, 2012
19. 19. Example 2 Find each measure. a. 180 - 60 = 120 120 ÷ 2 = 60 b. PRWednesday, February 8, 2012
20. 20. Example 2 Find each measure. a. 180 - 60 = 120 120 ÷ 2 = 60 = 60° b. PRWednesday, February 8, 2012
21. 21. Example 2 Find each measure. a. 180 - 60 = 120 120 ÷ 2 = 60 = 60° b. PR Since all three angles will be 60°, this is an equilateral triangle, so PR = 5 cm.Wednesday, February 8, 2012
22. 22. Example 3 Find the value of each variable.Wednesday, February 8, 2012
23. 23. Example 3 Find the value of each variable. 6y + 3 = 8y − 5Wednesday, February 8, 2012
24. 24. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 − 6y − 6yWednesday, February 8, 2012
25. 25. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 − 6y − 6y 3 = 2y − 5Wednesday, February 8, 2012
26. 26. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 − 6y − 6y 3 = 2y − 5 +5 +5Wednesday, February 8, 2012
27. 27. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 − 6y − 6y 3 = 2y − 5 +5 +5 8 = 2yWednesday, February 8, 2012
28. 28. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 − 6y − 6y 3 = 2y − 5 +5 +5 8 = 2y 2 2Wednesday, February 8, 2012
29. 29. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 − 6y − 6y 3 = 2y − 5 +5 +5 8 = 2y 2 2 y=4Wednesday, February 8, 2012
30. 30. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 4x − 8 = 4x − 8 − 6y − 6y 3 = 2y − 5 +5 +5 8 = 2y 2 2 y=4Wednesday, February 8, 2012
31. 31. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 4x − 8 = 4x − 8 − 6y − 6y − 4x + 8 − 4x + 8 3 = 2y − 5 +5 +5 8 = 2y 2 2 y=4Wednesday, February 8, 2012
32. 32. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 4x − 8 = 4x − 8 − 6y − 6y − 4x + 8 − 4x + 8 3 = 2y − 5 0=0 +5 +5 8 = 2y 2 2 y=4Wednesday, February 8, 2012
33. 33. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 4x − 8 = 4x − 8 − 6y − 6y − 4x + 8 − 4x + 8 3 = 2y − 5 0=0 +5 +5 Now what? 8 = 2y 2 2 y=4Wednesday, February 8, 2012
34. 34. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 4x − 8 = 4x − 8 − 6y − 6y − 4x + 8 − 4x + 8 3 = 2y − 5 0=0 +5 +5 Now what? 8 = 2y 4x − 8 = 60 2 2 y=4Wednesday, February 8, 2012
35. 35. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 4x − 8 = 4x − 8 − 6y − 6y − 4x + 8 − 4x + 8 3 = 2y − 5 0=0 +5 +5 Now what? 8 = 2y 4x − 8 = 60 2 2 +8 +8 y=4Wednesday, February 8, 2012
36. 36. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 4x − 8 = 4x − 8 − 6y − 6y − 4x + 8 − 4x + 8 3 = 2y − 5 0=0 +5 +5 Now what? 8 = 2y 4x − 8 = 60 2 2 +8 +8 y=4 4x = 68Wednesday, February 8, 2012
37. 37. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 4x − 8 = 4x − 8 − 6y − 6y − 4x + 8 − 4x + 8 3 = 2y − 5 0=0 +5 +5 Now what? 8 = 2y 4x − 8 = 60 2 2 +8 +8 y=4 4x = 68 4 4Wednesday, February 8, 2012
38. 38. Example 3 Find the value of each variable. 6y + 3 = 8y − 5 4x − 8 = 4x − 8 − 6y − 6y − 4x + 8 − 4x + 8 3 = 2y − 5 0=0 +5 +5 Now what? 8 = 2y 4x − 8 = 60 2 2 +8 +8 y=4 4x = 68 x = 17 4 4Wednesday, February 8, 2012
39. 39. Check Your Understanding Check out p. 287 #1-8 and see if you have an idea of what to do with these problemsWednesday, February 8, 2012
40. 40. Problem SetWednesday, February 8, 2012
41. 41. Problem Set p. 287 #9-31 odd (skip 27), 47, 56, 61 “We have, I fear, confused power with greatness.” - Stewart L. UdallWednesday, February 8, 2012