Proving Equality in a Parallelogram

Angles, Segments, Triangles, Statements, Reasons

Given: ABCD is a parallelogram. Diagonals AC, BD intersect at E. Prove: AE = CE and BE = DE

Final answer:

To prove AE = CE and BE = DE, we can use the fact that ABCD is a parallelogram and the diagonals AC and BD intersect at point E.

Explanation:

To prove that AE = CE and BE = DE, we will use the fact that ABCD is a parallelogram and the diagonals AC and BD intersect at point E.

First, since ABCD is a parallelogram, opposite sides are congruent. Hence, AB = CD and BC = AD.

Now, consider triangles ABE and CDE. These triangles share the side BE and have corresponding congruent angles at B and E. Therefore, by the Side-Angle-Side (SAS) congruence criterion, we can conclude that AE = CE and BE = DE.

What is the given information in the question? The given information states that ABCD is a parallelogram with diagonals AC and BD intersecting at point E.
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