Q146 of 158 Page 159

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?

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°


More from this chapter

All 158 →
144

ABC is an isosceles triangle with AB = AC and D is the mid-point of base BC (Fig. 6.48).

A. State three pairs of equal parts in the triangles ABD and ACD.


B. Is ∆ABD ≅ ∆ACD. If so why?


 145

In Fig. 6.49, it is given that LM = ON and NL = MO

A. State the three pairs of equal parts in the triangles NOM and MLN.


B. Is ∆NOM ≅ ∆MLN. Give reason?


 147

If ∆PQR and ∆SQR are both isosceles triangle on a common base QR such that P and S lie on the same side of QR. Are triangles PSQ and PSR congruent? Which condition do you use?

 148

In Fig. 6.50, which pairs of triangles are congruent by SAS congruence criterion (condition)? If congruent, write the congruence of the two triangles in symbolic form.