Math  /  Geometry

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Given: DE\overline{D E} bisects BDC\angle B D C and DE\overline{D E} bisects BEC\angle B E C. Prove: ABEACE\angle A B E \cong \angle A C E.
Note: the segment AEA E is a straight segment. Answer Attempt 1 out of 2

Studdy Solution
Use congruent angles and supplementary angles to prove ABEACE \angle ABE \cong \angle ACE : - Since AE \overline{AE} is a straight line, ABE+BED=180 \angle ABE + \angle BED = 180^\circ and ACE+CED=180 \angle ACE + \angle CED = 180^\circ . - From Step 2, BED=CED \angle BED = \angle CED . - Therefore, ABE=180BED \angle ABE = 180^\circ - \angle BED and ACE=180CED \angle ACE = 180^\circ - \angle CED . - Since BED=CED \angle BED = \angle CED , it follows that ABE=ACE \angle ABE = \angle ACE .
The proof is complete, and we have shown that:
ABEACE \angle ABE \cong \angle ACE

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