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If a triangle and a parallelogram are o...

If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram.

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To prove that the area of triangle \( \triangle ABP \) is equal to half the area of parallelogram \( ABCD \) when both are on the same base \( AB \) and between the same parallels, we can follow these steps: ### Step 1: Understand the Given Information We have a triangle \( \triangle ABP \) and a parallelogram \( ABCD \) that share the same base \( AB \) and are situated between the same parallel lines. ### Step 2: Draw the Diagram Draw the parallelogram \( ABCD \) with base \( AB \) and the triangle \( \triangle ABP \) such that point \( P \) lies above line \( AB \). Draw lines \( PN \) and \( DM \) perpendicular to \( AB \) from points \( P \) and \( D \) respectively. ...
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