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    Mathematics
    Grade9
    Easy

    Question

    Given that ∠A = ∠P and AC = PR. Then, which of the following conditions are true for Δ PQR and Δ ABC to be congruent

    1. BC = QR by ASS criteria
    2. BC = QR by SSA criteria
    3. AB = PQ by SAS criteria
    4. AB = PQ by SSA criteria

    hintHint:

    If two sides and the included angle of a triangle are equal to the two sides and the included angle of another triangle, then the two triangles are said to be congruent by SAS congruence criteria.
    One Side and angle is already given the possibilities are of congruency are  ASA (or) SAS rules.

    The correct answer is: AB = PQ by SAS criteria

      If two sides and the included angle of a triangle are equal to the two sides and the included angle of another triangle, then the two triangles are said to be congruent by SAS congruence criteria. Only SAS congruence criteria hold true not ASS or SSA rule.
      In Δ PQR and Δ ABC,
      ∠P = ∠A  (given),
      AC = PR  (given),
      Δ PQR and Δ ABC will be congruent by SAS rule only when AB = PQ.

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