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Question
Triangles DEF and LMN are both isosceles with DE = DF and LM = LN, respectively. If DE = LM and EF = MN, then, are the two triangles congruent? Which condition do you use? If ∠E = 40°, what is the measure of ∠N?
Solution
Here, DE = DF ......(i)
LM = LN ......(ii)
And DE = LM ......(iii)
From equations (i), (ii) and (iii), we get DE = DF = LM = LN
In ΔDEF and ΔLMN, DE = LM ......(Given)
EF = MN ......(Given)
DF = LN ......(Proved above)
By SSS congruence criterion, ΔDEF ≅ ΔLMN
∴ ∠E = ∠M ......[By CPCT]
∠M = 40°
Also, ∠M = ∠N ......[∵ ∠M = ∠N and angles opposite to equal sides are equal]
⇒ ∠N = 40°
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