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Warm up: Classify each triangle by its angles and sides. 1. 2. 60° 45° 60° 45° 60° 3. Triangle ABC has angles that measure 110, 50 and 20. Classify the triangle by its angles. 4. Triangle RST has sides that measure 3 feet, 4 feet and 5 feet. Classify the triangle by it sides. 5. Triangle KLM is an equilateral triangle in which KL = 3x 2, LM = x + 8 and KM = 2x +3. Find the measure of each side. Dec 79:29 AM OBJECTIVE: You will learn to use the Angle Sum Theorem. Section 52 __________________ Angle Sum Theorem The sum of the measures of the angles of a triangle is 180. Example 1: Find m T in RST. R 54° 67° S T Dec 79:29 AM 1 Example 2: Find the value of each variable in DCE. E B y° C 85° x° 55° A D Dec 79:29 AM Theorem 5 2 The acute angles of a right triangle are complementary. Example 3: Find m A and m B in right triangle ABC. C A 2x° 3x° B Dec 79:29 AM 2 equiangular triangle Theorem 53 The measure of each angle of an equiangular triangle is 60. Dec 79:30 AM Guided Practice: 1. Choose the numbers that are not measures of the three angles of a triangle. a. 10, 20, 150 b. 30, 60, 90 c. 40, 70, 80 d. 45, 55, 80 2. Is it possible to have two obtuse angles in a triangle? Why or why not? Dec 79:30 AM 3 Find the value of each variable. 3. 4. 68° 30° x° 58° y° y° Dec 79:31 AM 5. 63° a° b° 50° 6. The measures of the angles of a triangle are 2x, 3x and 4x. Find the measure of each angle. Dec 79:31 AM 4 Do you have any Vocab questions? OBJECTIVE: HOMEWORK: p. 196 197 # 8 20, 22 30 even Dec 79:31 AM 5