Nothing is impossible, the word itself says “I’m possible”! – **Audrey Hepburn**

# Lecture - 7 Chapter 6 Triangles

**NCERT Exercise 6.3 (Part 1)**

**Question 10.** CD and GH are respectively the bisectors of ∠ ACB and ∠ EGF such that D and H lie on sides AB and FE of ∆ ABC and ∆ EFG respectively. If ∆ ABC ~ ∆ FEG, show that:

(i) \( \frac{CD}{AC} = \frac{GH}{FG} \)

(ii) ∆ DCB ~ ∆ HGE

(iii) ∆ DCA ~ ∆ HGF

**Question 11.** In Fig. 6.40, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ∆ ABD ~ ∆ ECF.

**Question 13.** D is a point on the side BC of a triangle ABC such that ∠ ADC = ∠ BAC. Show that CA^{2} = CB.CD

**Question 15.** A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

**Question 16. **If AD and PM are medians of triangles ABC and PQR, respectively where ∆ ABC ~ ∆ PQR, prove that \( \frac{AB}{PQ} = \frac{AD}{PM} \)

NCERT Exercise 6.3 (Part 2)

Question 12. Sides AB and BC and median AD of a triangle ABC are respectively proportional to sides PQ and QR and median PM of ∆ PQR (see Fig. 6.41). Show that ∆ ABC ~ ∆ PQR.

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