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Lesson 3.4 TOPIC/Objective: To use angles to tell whether triangles are similar. Essential Question: How can you use angles to tell if triangles are similar. Example: The triangles have two pairs of congruent angles. The 3rd angle in each triangle must be 55⁰, therefore the triangles are similar. Example: Solve for x and y in each triangle 63 + 63 + y = 180 126 + y = 180 y = 54 Both triangles have angles of 54, 63, 63 Similar Example: 38 + y + 90 = 180 128 + y = 180 y = 52 90, 42, 48 38, 52, 90 Only one angle is the same. Not Similar Example: You place a mirror on the ground 6 feet from the lamppost. You move back 3 feet and see the top of the lamppost in the mirror. You are 5 feet tall. What is the height of the lamppost? 5ft 3ft The triangles are similar because two angles are the same, making all angles the same. The light pole is 10 ft. tall 5 𝑥 = 3 6 3x = 30 X = 10 6ft