in the given figure angle b is equal to angle c show that ae is greater than af.
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Let’s consider ∆ EDB,
∠ABC = ∠EDB + ∠BED …. [∵ exterior angles is sum of two non-adjacent interior angles]
⇒ ∠ABC > ∠BED
∵ ∠BED = ∠AEF as they are vertically opposite angles
∴ ∠ABC > ∠AEF …….. (i)
Now, let’s consider ∆ FDC,
∠AFE = ∠FDC +∠FCD …. [∵ exterior angles is sum of two non-adjacent interior angles]
⇒ ∠AFE > ∠FCD
⇒ ∠AFE > ∠ABC ……(ii) [∵ ∠B = ∠C given in the question]
From (i) & (ii), we can write,
∠AFE > ∠AEF
∵ A side opposite to greater angle is always greater and vice-versa.
∴ AE > AF
Hence proved
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