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Question
In the following figure, CD || AE and CY || BA. Prove that ar (CBX) = ar (AXY).
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Solution
Given: In the following figure, CD || AE and CY || BA
To prove: ar (ΔCBX) = ar (ΔAXY) .
Proof: We know that, triangles on the same base and between the same parallels are equal in areas.
Here, ΔABY and ΔABC both lie on the same base AB and between the same parallels CY and BA.
ar (ΔABY) = ar (ΔABC)
⇒ ar (ABX) + ar (AXY) = ar (ABX) + ar (CBX)
⇒ ar (AXY) = ar (CBX) ...[Eliminating ar (ABX) from both sides]
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