**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.3 Question 14**

**14.** Sides AB, AC and median AD of a triangle ABC are respectively proportional to sides PQ, PR and median PM of another triangle PQR. Show that ~

**Solution:**

**Given:**

**Construction: **In **, **extend median AD such that AD = DE. Join B and E and then join C and E.

In , extend median PM such that PM = MS. Join Q and S and then join R and S.

**To Prove: ** ~

**Proof: **We know that AD = DE by construction and also BD = DC which is given.

Therefore, diagonals of quadrilateral ABEC bisect each other at point D which makes quadrilateral ABEC a parallelogram.

Therefore, AB = CE and BE = AC **{Opposite sides of parallelogram are equal}** **(1)**

Similarly, QS = PR and PQ = RS. ** (2)**

We have,

From **(1)** and **(2)**, we can say that

**(3)**

From **(3), **we can say that ~

**{Triangles are similar if the corresponding sides of triangles are proportional}**

Therefore, {Corresponding angles of similar triangles are equal} **(4)**

Similarly, we can prove that **(5)**

Adding **(4)** and **(5)**, we can say that

**(6)**

But, we also have ** {Given}** **(7) **

From **(6)** and **(7)**, we can say that from **SAS** similarity criterion, ~

**Hence Proved**