Question

prove that if all sides of a parallelogram are equal then each diagonal is the perpendicular bisector of the other​

Answer 1

Answer:

Explanation is in the picture.

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Answer 2

Answer:

Proved Diagonal are Perpendicular Bisectors

Step-by-step explanation:

Concept= Congruency of Triangle

Given= Parallelogram

To find= Prove Diagonal is perpendicular bisectors

Explanation= Take parallelogram ABCD draw diagonals to AC and BD. Let the point of intersection of diagonals be P. Since each side of Parallelogram is equal, we compare ΔCDP and ΔABP.

=> AB=CD

=> ∠CDP = ∠ABP( Alt. Interiors)

=> ∠BAP=∠DCP( Alt. Interiors)

∴ ΔCDP and ΔABP are congruent.

similarly ΔBPC and ΔDPC are congruent.

∴ ∠DPC =∠BPC, we find angle BPC

DPC+BPC=180°

2BPC=180°

BPC=90°

since angle BPC is 90 and DPC is same .... we proved  that diagonals are the perpendicular bisectors of each other.

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