Little minds are tamed and subdued by misfortune; but great minds rise above it. – **Washington Irving**

# Lecture - 3 Chapter 6 Triangles

**NCERT Exercise 6.2**

**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

**Question 3.** In Fig. 6.18, if LM || CB and LN || CD, prove that \frac {AM}{AB} = \frac{AN}{AD}

**Question 4.** In Fig. 6.19, DE || AC and DF || AE. Prove that \frac{BF}{BE} = \frac{FE}{EC}

**Question 5.** In Fig. 6.20, DE || OQ and DF || OR. Show that EF || QR.

**Question 6.** In Fig. 6.21, A, B and C are points on OP, OQ and OR respectively such that AB || PQ and AC || PR. Show that BC || QR.

**Question 7.** Using Theorem 6.1, 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).

**Question 8.** Using Theorem 6.2, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).