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HELP ASAP!!!!!!!!!!

Given: ABCD is a parallelogram, BE bisects AC and DF bisects AC.
Prove: triangle BEC is congruent to triangle DFA.

HELP ASAP!!!!!!!!!! Given: ABCD is a parallelogram, BE bisects AC and DF bisects AC-example-1
User StefanTo
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1 Answer

9 votes

Answer:

1.) & 2.) BC and AD are congruent and parallel because in parallelogram opposite sides are equal and parallel

4.) <BCE≅<DAF because they are alternating interior angles bisected by line CA

5.) & 6.) The line BE/DF which bisects the <B/<D iS perpendicular to diagonal CA which forms the right angle

7.) Because sum of any two adjacent angles are 180
8.) This follows ASA Postulate which means that if 2 pair of angles is congruent given that they share a same side, the triangle formed will also be congruent.

Explanation:

Take the side CA as the same side of both triangles. This side also participates on the aforementioned angles on the given. The angles <BCE≅<DAF shares the side CA which makes the angles <DFA and <BEC congruent to each other. Therefore, the two right triangles are congruent

User AmitF
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