If two sides ABAB and BC,BC, and the median ADAD of △ABC△ABC are correspondingly equal to the two sides PQPQ and QR,QR, and the median PMPM of △PQR.△PQR. Prove that △ABC≅△PQR.△ABC≅△PQR.
Answer:
- We are given that AB=PQ, BC=QR, and AD=PM.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.△ABC≅△PQR.
- It is given that [Math Processing Error] Now, in △ABD and △PQM, we have [Math Processing Error]
- As corresponding parts of congruent triangles are equal, we have ∠B=∠Q …(2)
- In △ABC and △PQR, we have [Math Processing Error]
Hence Proved.