Tue August 07, 2012 By:

prove two triangles are congruent if aas,so the therom aas

Expert Reply
Tue August 07, 2012
Given: Two angles of two triangles are congruent. Also, one side, not included between these two angles are also congruent.
To Prove: The two triangles are congruent.
Let ABC and PQR be the two triangles such that angle A = angle P
angle B = angle Q
and BC = QR
Now, using angle sum property, we have:
angle C = 180 - (angle A + angle B)
            = 180 - (angle P + angle Q)
            = angle R
Thus, we have:
angle B = angle Q
angle C = angle R
Hence, by ASA congruence criterion, the two triangles ABC and PQR are congruent.
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