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°