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?

Answer 1

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°