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Question
In triangles ABC and PQR, ∠A = ∠P, BC = QR and ∠B = ∠Q, then they are congruent according to which all criteria?
In triangles ABC and PQR, ∠A = ∠P, BC = QR and ∠B = ∠Q, then they are congruent according to which all criteria?
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Solution
The correct options are
B A.S.A. criteria
D A.A.S. criteria
∠BAC = ∠QPR [Given]
BC = QR [Given]
∠ABC = ∠PQR [Given]
Since two angles of both the triangles are equal, the third angle will also be equal.
Hence,
∠BCA = ∠QRP
Therefore, the two triangles are congruent by AAS and ASA both.
B A.S.A. criteria
D A.A.S. criteria
∠BAC = ∠QPR [Given]
BC = QR [Given]
∠ABC = ∠PQR [Given]
Since two angles of both the triangles are equal, the third angle will also be equal.
Hence,
∠BCA = ∠QRP
Therefore, the two triangles are congruent by AAS and ASA both.
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