Question

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

Answer 1

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

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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.

Answer 2

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