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# Geometry section 4-1 1112

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Classifying Triangles

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• ### Geometry section 4-1 1112

1. 1. Chapter 4 Congruent TrianglesMonday, January 30, 2012
2. 2. Section 4-1 Classifying TrianglesMonday, January 30, 2012
3. 3. Essential Questions How do you identify and classify triangles by angle measures? How do you identify and classify triangles by side measures?Monday, January 30, 2012
4. 4. Vocabulary 1. Acute Triangle: 2. Equiangular Triangle: 3. Obtuse Triangle: 4. Right Triangle: 5. Equilateral Triangle:Monday, January 30, 2012
5. 5. Vocabulary 1. Acute Triangle: A triangle in which all three angles have a measure of less than 90 degrees 2. Equiangular Triangle: 3. Obtuse Triangle: 4. Right Triangle: 5. Equilateral Triangle:Monday, January 30, 2012
6. 6. Vocabulary 1. Acute Triangle: A triangle in which all three angles have a measure of less than 90 degrees 2. Equiangular Triangle: A triangle in which all three angles have a measure of 60 degrees, thus making them all equal 3. Obtuse Triangle: 4. Right Triangle: 5. Equilateral Triangle:Monday, January 30, 2012
7. 7. Vocabulary 1. Acute Triangle: A triangle in which all three angles have a measure of less than 90 degrees 2. Equiangular Triangle: A triangle in which all three angles have a measure of 60 degrees, thus making them all equal 3. Obtuse Triangle: A triangle in which one of the angles has a measure greater than 90 degrees 4. Right Triangle: 5. Equilateral Triangle:Monday, January 30, 2012
8. 8. Vocabulary 1. Acute Triangle: A triangle in which all three angles have a measure of less than 90 degrees 2. Equiangular Triangle: A triangle in which all three angles have a measure of 60 degrees, thus making them all equal 3. Obtuse Triangle: A triangle in which one of the angles has a measure greater than 90 degrees 4. Right Triangle: A triangle in which one of the angles has a measure of 90 degrees 5. Equilateral Triangle:Monday, January 30, 2012
9. 9. Vocabulary 1. Acute Triangle: A triangle in which all three angles have a measure of less than 90 degrees 2. Equiangular Triangle: A triangle in which all three angles have a measure of 60 degrees, thus making them all equal 3. Obtuse Triangle: A triangle in which one of the angles has a measure greater than 90 degrees 4. Right Triangle: A triangle in which one of the angles has a measure of 90 degrees 5. Equilateral Triangle: A triangle in which all three sides have the same measureMonday, January 30, 2012
10. 10. Vocabulary 6. Isosceles Triangle: 7. Scalene Triangle:Monday, January 30, 2012
11. 11. Vocabulary 6. Isosceles Triangle: A triangle in which at least two sides have the same measure 7. Scalene Triangle:Monday, January 30, 2012
12. 12. Vocabulary 6. Isosceles Triangle: A triangle in which at least two sides have the same measure 7. Scalene Triangle: A triangle in which no two sides have the same measureMonday, January 30, 2012
13. 13. Example 1 Classify each triangle as acute, equiangular, obtuse, or right. a. b.Monday, January 30, 2012
14. 14. Example 1 Classify each triangle as acute, equiangular, obtuse, or right. a. b. EquiangularMonday, January 30, 2012
15. 15. Example 1 Classify each triangle as acute, equiangular, obtuse, or right. a. b. Equiangular ObtuseMonday, January 30, 2012
16. 16. Example 2 Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning.Monday, January 30, 2012
17. 17. Example 2 Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning. RightMonday, January 30, 2012
18. 18. Example 2 Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning. Right m∠XYW + m∠WYZMonday, January 30, 2012
19. 19. Example 2 Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning. Right m∠XYW + m∠WYZ = 40°+50° = 90°Monday, January 30, 2012
20. 20. Example 3 The triangular truss is modeled for steel construction. Classify ∆JMN, ∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your reasoning. This figure is drawn to scale.Monday, January 30, 2012
21. 21. Example 3 The triangular truss is modeled for steel construction. Classify ∆JMN, ∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your reasoning. This figure is drawn to scale. JMN is obtuseMonday, January 30, 2012
22. 22. Example 3 The triangular truss is modeled for steel construction. Classify ∆JMN, ∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your reasoning. This figure is drawn to scale. JMN is obtuse m∠JNM > 90°Monday, January 30, 2012
23. 23. Example 3 The triangular truss is modeled for steel construction. Classify ∆JMN, ∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your reasoning. This figure is drawn to scale. JMN is obtuse m∠JNM > 90° JKO is rightMonday, January 30, 2012
24. 24. Example 3 The triangular truss is modeled for steel construction. Classify ∆JMN, ∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your reasoning. This figure is drawn to scale. JMN is obtuse m∠JNM > 90° JKO is right m∠JKO = 90°Monday, January 30, 2012
25. 25. Example 3 The triangular truss is modeled for steel construction. Classify ∆JMN, ∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your reasoning. This figure is drawn to scale. JMN is obtuse m∠JNM > 90° JKO is right OLN is equiangular m∠JKO = 90°Monday, January 30, 2012
26. 26. Example 3 The triangular truss is modeled for steel construction. Classify ∆JMN, ∆JKO, and ∆OLN as acute, equiangular, obtuse, or right. Explain your reasoning. This figure is drawn to scale. JMN is obtuse m∠JNM > 90° JKO is right OLN is equiangular m∠JKO = 90° All 3 angles have the same measureMonday, January 30, 2012
27. 27. Example 4 If point Y is the midpoint of VX and WY = 3 in., classify ∆VWY as equilateral, isosceles, or scalene. Explain your reasoning.Monday, January 30, 2012
28. 28. Example 4 If point Y is the midpoint of VX and WY = 3 in., classify ∆VWY as equilateral, isosceles, or scalene. Explain your reasoning. ∆VWY is scalene. Since Y is the midpoint of VX, we know that VY = YX = .5(VX) = 4.2 in. Along with the fact that WY = 3 in., we know all three sides of ∆VWY have different measures, thus making ∆VWY a scalene triangle.Monday, January 30, 2012
29. 29. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL.Monday, January 30, 2012
30. 30. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MKMonday, January 30, 2012
31. 31. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13Monday, January 30, 2012
32. 32. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13 25 = 5dMonday, January 30, 2012
33. 33. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13 25 = 5d d =5Monday, January 30, 2012
34. 34. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13 25 = 5d d =5 ML =12 − dMonday, January 30, 2012
35. 35. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13 25 = 5d d =5 ML =12 − d ML =12 −5Monday, January 30, 2012
36. 36. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13 25 = 5d d =5 ML =12 − d ML =12 −5 ML = 7 unitsMonday, January 30, 2012
37. 37. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13 25 = 5d d =5 ML =12 − d MK = 4d −13 ML =12 −5 ML = 7 unitsMonday, January 30, 2012
38. 38. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13 25 = 5d d =5 ML =12 − d MK = 4d −13 ML =12 −5 MK = 4(5)−13 ML = 7 unitsMonday, January 30, 2012
39. 39. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13 25 = 5d d =5 ML =12 − d MK = 4d −13 ML =12 −5 MK = 4(5)−13 ML = 7 units MK = 20 −13 = 7 unitsMonday, January 30, 2012
40. 40. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13 25 = 5d d =5 ML =12 − d MK = 4d −13 KL = d + 6 ML =12 −5 MK = 4(5)−13 ML = 7 units MK = 20 −13 = 7 unitsMonday, January 30, 2012
41. 41. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13 25 = 5d d =5 ML =12 − d MK = 4d −13 KL = d + 6 ML =12 −5 MK = 4(5)−13 KL = 5+ 6 ML = 7 units MK = 20 −13 = 7 unitsMonday, January 30, 2012
42. 42. Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13 25 = 5d d =5 ML =12 − d MK = 4d −13 KL = d + 6 ML =12 −5 MK = 4(5)−13 KL = 5+ 6 ML = 7 units MK = 20 −13 = 7 units KL =11 unitsMonday, January 30, 2012
43. 43. Check Your Understanding Peruse the following problems: p. 238 #1-14Monday, January 30, 2012
44. 44. Problem SetMonday, January 30, 2012
45. 45. Problem Set p. 239 #15-51 odd (skip 39), 56, 60, 75 “ Do not listen to those who weep and complain, for their disease is contagious.” - Og MandinoMonday, January 30, 2012