You don’t have to be great to start, but you have to start to be great. – **Zig Ziglar**

# Lecture - 6 Chapter 6 Triangles

**NCERT Exercise 6.3 (Part 1)**

** Question 1.** State which pairs of triangles in Fig. 6.34 are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form :

**Question 2.** In Fig. 6.35, ∆ ODC ~ ∆ OBA, ∠ BOC = 125° and ∠ CDO = 70°. Find ∠ DOC, ∠ DCO and ∠ OAB.

**Question 3.** Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that \( \frac{OA}{OB} = \frac{OC}{OD} \)

NCERT Exercise 6.3 (Part 2)

Question 4. In Fig. 6.36, \( \frac{QR}{QT} = \frac{QS}{PR} \) and ∠ 1 = ∠ 2. Show that ∆ PQS ~ ∆ TQR.

Question 5. S and T are points on sides PR and QR of ∆ PQR such that ∠ P = ∠ RTS. Show that ∆ RPQ ~ ∆ RTS.

Question 6. In Fig. 6.37, if ∆ ABE ≅ ∆ ACD, show that ∆ ADE ~ ∆ ABC.

Question 7. In Fig. 6.38, altitudes AD and CE of ∆ ABC intersect each other at the point P. Show that: (i) ∆ AEP ~ ∆ CDP

(ii) ∆ ABD ~ ∆ CBE

(iii) ∆ AEP ~ ∆ ADB

(iv) ∆ PDC ~ ∆ BEC

Question 8. E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ∆ ABE ~ ∆ CFB.

Question 9. In Fig. 6.39, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that:

(i) ∆ ABC ~ ∆ AMP

(ii) \( \frac{CA}{BC} = \frac{PA}{MP} \)