Respuesta :
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.
Parallelogram is a quadrilateral. Using the SSS (side-side-side) property for congruency and properties of parallelogram ΔABE and ΔCDE are congruent to each other.
What is parallelogram?
A parallelogram is a quadrilateral whose pair of opposite sides are in parallel and are of equal length. Also, the diagonals of a parallelogram bisect each other.
Given to us
ABCD is a parallelogram.
E is the point where the diagonals AC and BD meet.
In ΔABE and ΔCDE
As we know that the opposite sides of the parallelogram are of equal length, therefore,
AB = CD.
Also, we have discussed that the diagonal of the parallelogram bisect each other, therefore,
AE = EC
BE = ED
Hence, Using the SSS (side-side-side) property for congruency and properties of parallelogram ΔABE and ΔCDE are congruent to each other.
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