Question

In triangle LMN and triangle OPN, if triangle LMN = triangle NPO = 60°, LNM = 35° and LM = PO = 4 cm. Then check whether the triangle LMN is congruent to triangle PON or not.

Please answer I will mark you brainliest.​

Answer 1

The triangle LMN is congruent to triangle PON

GIVEN

In triangle LMN and triangle OPN, ∠ LMN = ∠NPO = 60°, ∠LNM = 35° and LM = PO = 4 cm.

TO FIND

Wether the traingle LMN is congruent to ΔPON

SOLUTION

We can simply solve the above problem as follows;

In ΔLMN and ΔPON

∠LMN = ∠NPO = 60° (GIVEN)

∠LMN = ∠PNO (Vertically opposite angles are equal)

∠MLN = 180 - (60 + 35) = 180 - 95 = 85°

∠PON = 180 - (60 + 35) = 85°

Therefore,

∠MLN = ∠PON

LM = PO (GIVEN)

By ASA congruency-

∆LMN ≅ ∆OPN.

Hence, The triangle LMN is congruent to triangle PON

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