If two sides AB and BC, and the median AD of △ABC are correspondingly equal to the two sides PQ and QR, and the median PM of △PQR. Prove that △ABC≅△PQR.
Answer:
- We are given that AB=PQ, BC=QR, and AD=PM.
Let us now draw the triangles and mark the equal sides and medians. - We need to prove that △ABC≅△PQR.
- It is given that BC=QR⟹12BC=12QR⟹BD=QM…(1) [As the median from a vertex of a triangle bisects the opposite side.] Now, in △ABD and △PQM, we have AD=PM[Given]AB=PQ[Given]BD=QM[From (1)]∴ △ABD≅△PQM[By SSS criterion]
- As corresponding parts of congruent triangles are equal, we have ∠B=∠Q …(2)
- In △ABC and △PQR, we have BC=QR[Given]AB=PQ[Given]∠B=∠Q[From (2)]∴ △ABC≅△PQR[By SAS criterion]
Hence Proved.