# NCERT Mathematics Class 10 Exemplar Ch 6 Triangles Part 4

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**EXERCISE 6.3**

1. In a Δ PQR, and M is a point on side PR such that . Prove that

2. Find the value of x for which in Fig. 6.8.

Answer: x = 2

3. In Fig. 6.9, if and , then prove that .

4. Diagonals of a trapezium PQRS intersect each other at the point O, and RS. Find the ratio of the areas of triangles POQ and ROS.

Answer: 9:1

5. In Fig. 6.10, if and AC and PQ intersect each other at the point O, prove that . AP.

6. Find the altitude of an equilateral triangle of side .

Answer:

7. If , , , and , find the perimeter of Δ ABC.

Answer: