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Question
ABCD is a square. E and F are respectively the mid-points of BC and CD. If R is the mid-point of EF (Figure), prove that ar (AER) = ar (AFR)
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Solution
Given: In square ABCD, E and F are the mid-points of BC and CD respectively. Also, R is the mid-point of EF.
To prove: ar (AER) = ar (AFR).
Construction: Draw AN ⊥ EF.
Proof: ar (ΔAER) = `1/2` × Base × Height
= `1/2 xx ER xx AN`
= `1/2 xx FR xx AN` ...[∵ R is the mid-point of EF, so ER = FR]
= ar (ΔAFR)
Hence proved.
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