Question

if AD and PM are medians of triangles ABC and PQR, respectively where triangle ABC is similar to triangle PQR,prove that AB/PQ=AD/PM

Answer 1

I hope it will help you

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

For better understanding of the solution, see the attached figure of the problem :

Given : ΔABC ~ ΔPQR

Since, sides of the similar triangles are proportional to each other

$\implies \frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}\\\\\implies \frac{AB}{PQ}=\frac{2BD}{2QM}\:\:\text{(Because AD and PM are medians)}\\\\\implies \frac{AB}{PQ}=\frac{BD}{QM}..........(1)$

In ΔABD and ΔPQM

$\frac{AB}{PQ}=\frac{BD}{QM}\:\:\text{ ( From equation (1) )}$

∠B = ∠Q

Hence, By SAS similarity postulate, ΔABD ~ ΔPQM

$\frac{AB}{PQ}=\frac{AD}{PM}$

Hence Proved.