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Geometry Section 8.2 Proving Triangles Similar by AA What you will learn: 1. Use the Angle-Angle Similarity theorem 2. Solve real-life problems To say that two polygons are similar by the definition of similarity, we would need to know that all corresponding sides are _______________ proportional and all corresponding angles are ____________. congruent The following theorem gives us easier method for determining if two triangles are similar. Angle-Angle (AA) Similarity Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the triangles are similar. Examples: Determine if the triangles are similar. If so, write a similarity statement and identify the theorem used. AA EAC ~ BDC AA ABC ~ EDC Similar triangles can be used to find the height of objects. Consider these two methods. s similar by AA Pole' s height Pole' s Shadow Person' s height Person' s shadow s similar by AA Distance from Tree' s height tree to mirror Person' s height Distance from person to mirror Example: Betty needs to estimate the height of a maple tree. She puts one end of a 100-foot tape measure at the base of the tree and walks away from the tree. At the 40-foot mark, she puts a mirror flat on the ground. Continuing to walk away from the tree, she eventually sees the top of the tree in the mirror and notes that she is 48 feet 8 inches away from the tree. If Betty is 5’ 3” tall, estimate the height of the tree to the nearest foot. 5.25 8.667 tree 40 8.667tree 210 tree 24.230 ft 5.25 8.667 40 48.667 Example: Archie is 6’ 5” tall. If he casts a shadow that is 5’ 2” long at the same time a flag pole casts a shadow 27’ 7” long, estimate the height of the flag pole to the nearest foot. 5.167 6.417 27.583 Pole 6.417 5.167 pole 177.000 pole 34.256 ft 5.167 27.583 HW: pp 431 – 432 / 3 – 18, 21, 23 - 26