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EXAMPLE 4

GIVEN. AB DE , A C DF , BC EF. D A. PROVE. Add BC and EF to the diagram. In the construction, AB , DE , AC , and DF are all determined by the same compass setting, as are BC and EF . So, you can assume the following as given statements. EXAMPLE 4.

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EXAMPLE 4

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  1. GIVEN AB DE, AC DF, BC EF DA PROVE Add BCand EFto the diagram. In the construction, AB, DE, AC, and DFare all determined by the same compass setting, as are BCand EF. So, you can assume the following as given statements. EXAMPLE 4 Prove a construction Write a proof to verify that the construction for copying an angle is valid. SOLUTION

  2. Show that CAB FDE, so you can conclude that the corresponding parts Aand Dare congruent. Plan For Proof STATEMENTS REASONS AB DE Given D A Corresp. parts of AC DF, BC EF are . SSS Congruence Postulate FDE CAB EXAMPLE 4 Prove a construction Plan in Action

  3. AC and AB for Example 4 GUIDED PRACTICE Look back at the construction of an angle bisector in Explore 4 on page 34. What segments can you assume are congruent? SOLUTION

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