**Triangles**

**Question 1.****In the given figure (i) and (ii), DE || BC. Find EC in (i) and AD in (ii).**

Solution:

**Question 2.****E and F are points on the sides PQ and PR respectively of a ∆PQR. For each of the following cases, state whether EF || QR:**

**(i)** PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm**(ii)** PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm**(iii)** PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm

**Solution:**

**Question 3.**

**In the given figure, if LM || CB and LN || CD.**

Prove that

**Solution:**

**Question 4.****In the given figure, DE || AC and DF || AE.**

Prove that

**Solution:**

**Question 5.****In the given figure, DE || OQ and DF || OR. Show that EF || QR.**

Solution:

**Question 6.****In the given figure, A, B, and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.**

Solution:

**Question 7.****Using B.P.T., prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in class IX)**

**Solution:**

The given figure shows an ∆ABC in which D is the mid-point of AB.

**Question 8.****Using converse of B.P.T., prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that your have done it in class IX)**

**Solution:**

The given figure shows a ΔABC in which D and E are mid-points of sides AB and AC respectively.

**Question 9.****ABCD is a trapezium in which AB || DC and its diagonals intersect each other at the point O. Show that **

**Solution:**

**Question 10.****The diagonals of a quadrilateral ABCD intersect each other at the point O such that Show that ABCD is a trapezium.**

**Solution:**