UPSKILL MATH PLUS
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Learn more1. In triangles \(ABC\) and \(PQR\), \(\angle A = \angle Q\) and \(\angle B = \angle R\). Which side of \(\triangle PQR\) should be equal to side \(AB\) of \(\triangle ABC\) so that the two triangles are congruent? Give reason for your answer.
2. In triangles \(ABC\) and \(PQR\), \(\angle A = \angle Q\) and \(\angle B = \angle R\). Which side of \(\triangle PQR\) should be equal to side \(BC\) of \(\triangle ABC\) so that the two triangles are congruent? Give reason for your answer.
Solution:
1. Consider \(\triangle ABC\) and \(\triangle PQR\).
\(\angle A = \angle Q\) [Given]
\(\angle B = \angle R\) [Given]
Therefore, by axiom \(AB = QR\)
Thus, triangles \(ABC\) and \(PQR\) are congruent by ASA congruence rule if the side \(AB\) is equal to
2. Consider \(\triangle ABC\) and \(\triangle PQR\).
\(\angle A = \angle Q\) [Given]
\(\angle B = \angle R\) [Given]
Therefore, by , \(BC = RP\)
Thus, triangles \(ABC\) and \(PQR\) are congruent by AAS congruence rule if the side \(BC\) is equal to
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