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Proving Triangle Congruence and Midpoints with Bisectors in Geometry

This document presents a series of geometric proofs involving triangle congruence, midpoint relationships, and angle bisectors. Utilizing principles such as the Midpoint Theorem and Triangle Congruence Postulates, the proofs demonstrate that certain triangles are equal and that specific line segments bisect each other at designated points. Step-by-step reasoning is provided to showcase the logical progression of the proofs, helping students understand how to apply geometric concepts to solve problems effectively.

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Proving Triangle Congruence and Midpoints with Bisectors in Geometry

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  1. ab | bc and xy | yz x a Statements Reasons z b c y IF HL b a ad |dc and cb | ab, bc = ad, prove adc = cba c d z xw |wy and yz | wy, wa = ya, prove xwa = zya w w y y a a x xw |wy and yz | wy, a is the midpoint of wy, prove xwa = zya z x

  2. ac bisects db at e, ad = bc. Prove triangle ade = triangle bce a b e d c HOMEWORK --- HINT: These all use different postulates ad bisects bc at e. ab | bc , cd | bc. Prove abe = dce a a a c c c e e e b b b d e is the midpoint of ad and bc. . Prove abe = dce d ab | bc , cd |bc.. bc bisects ad at e. Prove be = ce. d

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