Q. 1464.3( 3 Votes )

# 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 :

Given: Triangles DEF and LMN are both isosceles

DE = DF and LM = LN, respectively.

If DE = LM and EF = MN

DE = DF and LM = LN

If DE = LM

Then putting value on both sides

We get

DF = LN

In Δ DEF and Δ LMN

DE = LM

DF = LN

EF = MN

⇒ Hence Δ DEF ≅ Δ LMN

Both triangles are congruent by SSS criterion

As both triangles are congruent

∠E = ∠M

∴ ∠M = 40°

As LMN is isosceles triangle having base angles are equal

∠M = ∠N

∴ ∠N = 40°

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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?

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