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MX AB . Explain why the triangles are similar. Write a similarity statement.

Because MX AB ,  AXM and  BXK are both right angles, so  AXM  BXK.  A  B because their measures are equal. AMX ~ BKX by the Angle-Angle Similarity Postulate (AA ~ Postulate). Proving Triangles Similar. LESSON 7-3. Additional Examples.

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MX AB . Explain why the triangles are similar. Write a similarity statement.

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  1. Because MX AB, AXM and BXK are both right angles, so AXMBXK.  A  B because their measures are equal. AMX ~ BKX by the Angle-Angle Similarity Postulate (AA ~ Postulate). Proving Triangles Similar LESSON 7-3 Additional Examples MX AB. Explain why the triangles are similar. Write a similarity statement. Quick Check

  2. YVZ WVX because they are vertical angles. VY VW 12 24 1 2 VZ VX 18 36 1 2 = = and = = , so corresponding sides are proportional. Therefore, YVZ ~ WVX by the Side-Angle-Side Similarity Theorem(SAS Similarity Theorem). Proving Triangles Similar LESSON 7-3 Additional Examples Explain why the triangles must be similar. Write a similarity statement. Quick Check

  3. Because ABCD is a parallelogram, AB || DC. XAW ZYW and AXW YZW because parallel lines cut by a transversal form congruent alternate interior angles. Therefore, AWX ~ YWZ by the AA ~ Postulate. WY WA WZ WX Corresponding sides of ~ triangles are proportional. = 10 4 WY 5 Substitute. = 10 4 Solve for WY. WY =  5 Proving Triangles Similar LESSON 7-3 Additional Examples ABCD is a parallelogram. Find WY. Use the properties of similar triangles to find WY. Quick Check WY = 12.5

  4. Draw the situation described by the example. TR represents the height of the tree, point M represents the mirror, and point J represents Joan’s eyes. Both Joan and the tree are perpendicular to the ground, so m JOM = mTRM, and therefore JOMTRM. The light reflects off a mirror at the same angle at which it hits the mirror, so JMOTMR. Proving Triangles Similar LESSON 7-3 Additional Examples Joan places a mirror 24 ft from the base of a tree. When she stands 3 ft from the mirror, she can see the top of the tree reflected in it. If her eyes are 5 ft above the ground, how tall is the tree? Use similar triangles to find the height of the tree.

  5. JOM ~ TRM AA ~ Postulate RM OM TR JO Corresponding sides of ~ triangles are proportional. = 24 3 TR 5 Substitute. = 24 3 TR 5 Solve for TR. =  5 TR = 40 Proving Triangles Similar LESSON 7-3 Additional Examples (continued) The tree is 40 ft tall. Quick Check

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