Mathematics
In the following figure, CE is drawn parallel to diagonal DB of the quadrilateral ABCD which meets AB produced at point E.
Prove that △ ADE and quadrilateral ABCD are equal in area.
Theorems on Area
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Answer
We know that,
Triangles on the same base and between the same parallel lines are equal in area.
△ BDE and △ BDC lie on the same base BD and along the same parallel lines DB and CE.
∴ Area of △ BDE = Area of △ BDC ……….(1)
From figure,
⇒ Area of △ ADE = Area of △ ADB + Area of △ BDE
⇒ Area of △ ADE = Area of △ ADB + Area of △ BDC [From equation (1)]
⇒ Area of △ ADE = Area of quadrilateral ABCD.
Hence, proved that △ ADE and quadrilateral ABCD are equal in area.
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