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Five-Minute Check (over Lesson 4–1) Then/Now New Vocabulary Theorem 4.1: Triangle Angle-Sum Theorem Proof: Triangle Angle-Sum Theorem Example 1: Real-World Example: Use the Triangle Angle-Sum Theorem Theorem 4.2: Exterior Angle Theorem Proof: Exterior Angle Theorem Example 2: Real-World Example: Use the Exterior Angle Theorem Corollaries: Triangle Angle-Sum Corollaries Example 3: Find Angle Measures in Right Triangles Over Lesson 4–1 Classify ΔRST . A. acute B. equiangular A B C 0% D D 0% B 0% A D. right C C. obtuse A. B. C. 0% D. Over Lesson 4–1 Find y___ if ΔRST is an isosceles triangle with ___ RS RT. A. 8 B. 10 C. 12 0% D 0% C 0% B 0% A D. 14 A. B. C. D. A B C D Over Lesson 4–1 Find x if ΔABC is an equilateral triangle. A. 2 B. 4 C. 6 0% D 0% C 0% B 0% A D. 8 A. B. C. D. A B C D Over Lesson 4–1 A. ΔABC B. ΔACB C. ΔADC 0% D 0% C 0% B 0% A D. ΔCAB A. B. C. D. A B C D Over Lesson 4–1 Classify ΔMNO as scalene, isosceles, or equilateral if MN = 12, NO = 9, and MO = 15. A. scalene B. isosceles A 0% 0% B C. equilateral A B C 0% C 1. 2. 3. Over Lesson 4–1 Which is not a classification for ΔFGH? A. acute B. scalene isosceles 0% 0% D equiangular 0% C D. A 0% B C. 1. 2. 3. 4. A B C D You classified triangles by their side or angle measures. (Lesson 4–1) • Apply the Triangle Angle-Sum Theorem. • Apply the Exterior Angle Theorem. • auxiliary line • exterior angle • remote interior angles • flow proof Use the Triangle Angle-Sum Theorem SOFTBALL The diagram shows the path of the softball in a drill developed by four players. Find the measure of each numbered angle. Understand Examine the information in the diagram. You know the measures of two angles of one triangle and only one measure of another. You also know that 1 and 2 are vertical angles. Use the Triangle Angle-Sum Theorem Plan Find m1 first because the measure of two angles of the triangle are known. Use the Vertical Angles Theorem to find m2. Then you will have enough information to find the measure of 3. Solve Triangle Angle-Sum Theorem Simplify. Subtract 117 from each side. Use the Triangle Angle-Sum Theorem 1 and 2 are congruent vertical angles. So, m2 = 63. Triangle Angle-Sum Theorem Simplify. Subtract 142 from each side. Answer: Therefore, m1 = 63, m2 = 63, and m3 = 38. Check The sums of the measures of the angles in each triangle should be 180. m1 + 43 + 74 = 63 + 43 + 74 or 180 m2 + m3 + 79 = 63 + 38 + 79 or 180 Find the measure of 3. A. 95 B. 75 C. 57 D. 85 0% D 0% C 0% B A 0% A. B. C. D. A B C D Use the Exterior Angle Theorem GARDENING Find the measure of FLW in the fenced flower garden shown. mLOW + mOWL= mFLW x + 32 = 2x – 48 Exterior Angle Theorem Substitution 32 = x – 48 Subtract x from each side. 80 = x Add 48 to each side. Answer: So, mFLW = 2(80) – 48 or 112. The piece of quilt fabric is in the shape of a right triangle. Find the measure of ACD. A. 30 B. 40 C. 50 D. 130 0% D 0% C 0% B A 0% A. B. C. D. A B C D Find Angle Measures in Right Triangles Find the measure of each numbered angle. Exterior Angle Theorem m1 = 48 + 56 Simplify. = 104 104 + m2 = 180 If 2 s form a linear pair, they are supplementary. Substitution 76 Subtract 104 from each side. Find Angle Measures in Right Triangles If 2 s form a right angle, they are complementary. m 3 = 90 – 48 Simplify. = 42 (90 – 34) + m2 + m 4 = 180 56 + 76 + m 4 = 180 132 + m4 = 180 48 Triangle Sum Theorem Substitution Simplify. Subtract 132 from each side. Find Angle Measures in Right Triangles m5 + 41 + 90 = 180 m5 + 143 = 180 49 Triangle Angle-Sum Theorem Simplify. Subtract 131 from each side. m1 = 104, m2 = 76, m 3 = 42, m4 = 48, m5 = 49 Find m3. A. 50 B. 45 0% B A 0% A B C 0% D D D. 130 A. B. C. 0% D. C C. 85

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