In △ABC and △PQR, we are given ∠A=∠P and AC=PR.
Which of the following options needs to be satisfied for △PQR and △ABC to be congruent?
- ABC = QR by ASS criteria
- BAB = PQ by SAS criteria
- CBC = QR by SSA criteria
- DAB = PQ by SSA criteria
Solution & Step-by-step Explanation
We are given:
One equal angle: ∠A=∠P
One equal adjacent side: AC=PR
For the triangles to be congruent using standard valid congruence criteria:
SAS (Side-Angle-Side) requires the angle to be included between the two corresponding sides.
The sides including ∠A are AB and AC.
The sides including ∠P are PQ and PR.
Since we already have AC=PR, adding AB=PQ satisfies the SAS congruence criteria. Note that ASS or SSA are not universally valid congruence criteria.
One equal angle: ∠A=∠P
One equal adjacent side: AC=PR
For the triangles to be congruent using standard valid congruence criteria:
SAS (Side-Angle-Side) requires the angle to be included between the two corresponding sides.
The sides including ∠A are AB and AC.
The sides including ∠P are PQ and PR.
Since we already have AC=PR, adding AB=PQ satisfies the SAS congruence criteria. Note that ASS or SSA are not universally valid congruence criteria.