# Lecture 7 Chapter 6 Class 10 Maths

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 CA2 = 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.