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Given: CE congruent DB, AEC congruent ADB
Prove: CEA congruent BDA

User Florian Bw
by
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1 Answer

4 votes

Answer:

See below, that CEA is congruent to BDA.

Explanation:

Based on the given information, we can draw the following diagram

C ------- E

/ \

/ \

/ \

/ \

A ------- E ------- B

D

We are given that CE is congruent to DB, and that angle AEC is congruent to angle ADB. We need to prove that angle CEA is congruent to angle BDA.

To do so, we can use the fact that the sum of angles in a triangle is 180 degrees. First, we can use the fact that angle AEC is congruent to angle ADB to write

angle AEC + angle CEA = angle ADB + angle BDA

We can rearrange this to get

angle CEA = angle BDA + angle AEC - angle ADB

Therefore, angle AEC is congruent to angle ADB, and side CE is congruent to side DB, so angle CEA must be congruent to angle BDA.

Hence, we have proved that CEA is congruent to BDA.

User Yazu
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8.6k points