Lecture-6

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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 :
Class 10 triangles exercise 6.3 Question 1 figure

Question 2. In Fig. 6.35, ∆ ODC ~ ∆ OBA, ∠ BOC = 125° and ∠ CDO = 70°. Find ∠ DOC, ∠ DCO and ∠ OAB.
Class 10 triangles exercise 6.3 Question 2 figure

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}

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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.
Class 10 triangles exercise 6.3 Question 4 figure

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.
Class 10 triangles exercise 6.3 Question 6 figure

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
Class 10 triangles exercise 6.3 Question 7 figure

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}
Class 10 triangles exercise 6.3 Question 9 figure