# P is any a point on diagonal BD of parallelogram ABCD. Let’s prove that triangle APD = triangle CPD.

Given.

P is any a point on diagonal BD of parallelogram ABCD

Formula used.

Area of triangle = × Base × Height In triangle APD and triangle CPD

As ABCD is a parallelogram

And BD is the diagonal

it divides both congruent triangles

Hence perpendicular of both the triangles are same

AX= CY

For any place of P on BD

The perpendicular of triangle will be same of as of triangle ADB and triangle CBD

Area of triangle APD = × AX × DP

Area of triangle CPD = × CY × DP

= × AX × DP

Area of triangle APD = Area of triangle CPD

triangle APD = triangle APD

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