Two triangles are similar. Prove that if sides in one pair of corresponding sides are congruent, then the triangles are congruent.
Given: The correspondence ∆ABC↔∆PQR is a similarity and AB ≅ PQ.
To prove: ∆ABC and ∆PQR are congruent.
Proof:
The correspondence ∆ABC↔∆PQR is a similarity.
Further, AB ≅ PQ
AB = PQ
AB = PQ, BC = QR, AC = PR
AB ≅ PQ, BC ≅ QR, AC ≅ PR
The correspondence ∆ABC↔∆PQR is a congruence by SSS theorem of congruence.
Hence, ∆ABC and ∆PQR are congruent.
AI is thinking…
Couldn't generate an explanation.
Generated by AI. May contain inaccuracies — always verify with your textbook.
such that 
. Prove that X, Y, Z are the mid-points of 
, 
, 
respectively.
such that 
are positive real numbers. A line passing through P and parallel to 
intersects 
in Q. Prove that (m + n)2 (area of ΔAPB) = m2(area of ΔABC)
, 
and 
respectively in ΔABC. Prove that the area of