Question

prove that if two angles and one side of a triangle are equal to two angles and one side of another triangle. the triangles are congruent. Also check if the given pair of triangles are congruent?​

Answer 1

Answer:

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Answer 2

Given : Two angles of triangles are equal and side not containing the angle is equal

To find : prove that triangles are congruent

Solution:

Let say Two triangles

ABC    &  PQR

∠A = ∠P

∠B = ∠Q

AC = PR   or  BC = QR

Sum of angles of triangle = 180°

=> ∠A + ∠B + ∠C = 180°

=> ∠C = 180° - ∠A - ∠B

=> ∠C = 180° - ∠P - ∠Q

=> ∠C = ∠R

Case 1 : AC = PR

Hence ∠A = ∠P  , AC = PR , ∠C = ∠R

Triangles are congruent using ASA  rule

ΔABC ≅  ΔPQR

Case 1 : BC = QR

Hence ∠B = ∠Q  , BC = QR , ∠C = ∠R

Triangles are congruent using ASA  rule

ΔABC ≅  ΔPQR

Hence triangles are congruent

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