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Question
In the following figure, if ΔABE ≅ ΔACD, show that ΔADE ∼ ΔABC.
Sum
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Solution
It is given that ΔABE ≅ ΔACD.
∴ AB = AC …(1) [CPCT]
And, AD = AE …(2) [CPCT]
⇒ `"AE"/"AB" = "AD"/"AC"` ...(3)
In ΔADE and ΔABC,
∵ `"AE"/"AB" = "AD"/"AC"` ...[Dividing equation 2 by 1]
∠A = ∠A ...[Common angle]
∴ ΔADE ∼ ΔABC ...[By SAS similarity criterion]
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