# 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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Basic Proportionality Theorem42 mins
Quiz | Criterion of Similarity of Triangle45 mins
Champ Quiz | Thales Theorem49 mins
How to Ace Maths in NTSE 2020?36 mins
NCERT | Strong Your Basics of Triangles39 mins
RD Sharma | Imp. Qs From Triangles41 mins
R.D Sharma | Solve Exercise -4.2 and 4.3FREE Class
R.D Sharma | Solve Exercise-4.545 mins
NCERT | Basic Proportionality Theorem22 mins
RD Sharma | Imp Qs Discussion- Triangles43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses