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2 years ago

ABCD is a parallelogram. E is the point where the diagonals AC and BD meet. Prove that triangle ABE is congruent to triangle CDE

Mathematics

2 answers:

iogann1982 [59]2 years ago

7 0

Answer:

Step-by-step explanation:

Given that ABCD is a parallelogram.

E is the point where the diagonals AC and BD meet.

Consider triangles ABE and CDE

Statement Reason

--------------------------------------------------------------------

1) AB =CD Opposite sides of a parallelogram

2) Angle ABE =

Angle EDC Alternate angles of two parallel lines

3) BE = DE Diagonals bisect each other in a parallelogram

Hence by SAS axiom the two triangles are congruent.

Darina [25.2K]2 years ago

5 0

ABCD is a parallelogram Given
AE=CE, BE=DE <span>The diagonals of a parallelogram are bisect each other
</span>∠AEB=∠CED Vertical angles are congruent
ΔABE is congruent to ΔCDE SAS theorem<span>
</span>

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