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Chapter 4 Congruent TrianglesMonday, January 30, 2012
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Section 4-1 Classifying TrianglesMonday, January 30, 2012
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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
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Vocabulary 1. Acute Triangle: 2. Equiangular Triangle: 3. Obtuse Triangle: 4. Right Triangle: 5. Equilateral Triangle:Monday, January 30, 2012
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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
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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
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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
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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
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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
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Vocabulary 6. Isosceles Triangle: A triangle in which at least two sides have the same measure 7. Scalene Triangle:Monday, January 30, 2012
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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
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Example 1 Classify each triangle as acute, equiangular, obtuse, or right. a. b.Monday, January 30, 2012
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Example 1 Classify each triangle as acute, equiangular, obtuse, or right. a. b. EquiangularMonday, January 30, 2012
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Example 1 Classify each triangle as acute, equiangular, obtuse, or right. a. b. Equiangular ObtuseMonday, January 30, 2012
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Example 2 Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning.Monday, January 30, 2012
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Example 2 Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning. RightMonday, January 30, 2012
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Example 2 Classify ∆XYZ as acute, equiangular, obtuse, or right. Explain your reasoning. Right m∠XYW + m∠WYZMonday, January 30, 2012
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Example 5 Find the measure of the sides of isosceles ∆KLM with base KL.Monday, January 30, 2012
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Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MKMonday, January 30, 2012
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Example 5 Find the measure of the sides of isosceles ∆KLM with base KL. ML = MK 12 − d = 4d −13Monday, January 30, 2012
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Check Your Understanding Peruse the following problems: p. 238 #1-14Monday, January 30, 2012
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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
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