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In this guide, we'll prove the validity of a construction for copying an angle using congruence principles. We focus on segments AB, DE, AC, and DF, which are determined by the same compass setting as segments BC and EF. By establishing that triangles CAB and FDE are congruent through the Side-Side-Side (SSS) Congruence Postulate, we can conclude that the corresponding angles A and D are also congruent. This proof reinforces the foundational concepts of angle construction and congruence in geometry.
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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
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
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
