Question

Prove that parallelogram on the same base and between the same parallelogram are equal by its area

Answer 1

Answer:

Note that there are two parallelograms ABCD and EE’CD on the same base DC and between the same parallels AE’ and DC. What can you say about their areas?

As ∆ADE ≅ ∆ A’ D’ E’

Therefore, Area (ADE) = Area (A’ D’ E’)

Also, Area (ABCD) = Area (ADE) + Area (EBCD)

= Area (A’D’E’) + Area (EBCD)

= Area (EE’CD)

So, the two parallelograms are equal in area.

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