Page 1 Exercise 4B 1. In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form: Sol: (i) We have: BAC = PQR = ABC = QPR = ACB = PRQ = QPR (ii) We have: But , EDF (Included angles are not equal) Thus, this triangles are not similar. (iii) We have: Also, ACB = PQR = - (iv) We have Page 2 Exercise 4B 1. In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form: Sol: (i) We have: BAC = PQR = ABC = QPR = ACB = PRQ = QPR (ii) We have: But , EDF (Included angles are not equal) Thus, this triangles are not similar. (iii) We have: Also, ACB = PQR = - (iv) We have - (v) A + (Angle Sum Property) 2. BOC = 115 0 and CDO = 70 0 . Find (i) DCO (ii) DCO (iii) OAB (iv) OBA. Sol: (i) It is given that DB is a straight line. Therefore, (ii) Therefore, (iii) - Therefore, (iv) - Therefore, Page 3 Exercise 4B 1. In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form: Sol: (i) We have: BAC = PQR = ABC = QPR = ACB = PRQ = QPR (ii) We have: But , EDF (Included angles are not equal) Thus, this triangles are not similar. (iii) We have: Also, ACB = PQR = - (iv) We have - (v) A + (Angle Sum Property) 2. BOC = 115 0 and CDO = 70 0 . Find (i) DCO (ii) DCO (iii) OAB (iv) OBA. Sol: (i) It is given that DB is a straight line. Therefore, (ii) Therefore, (iii) - Therefore, (iv) - Therefore, 3. If AB = 8cm, BO = 6.4cm, OC = 3.5cm and CD = 5cm, find (i) OA (ii) DO. Sol: (i) Let OA be X cm. - Hence, OA = 5.6 cm (ii) Let OD be Y cm - Hence, DO = 4 cm 4. In the given figure, if ADE = B, show that BE = 2.1cm and BC = 4.2cm, find DE. Sol: Given : Let DE be X cm - 5. The perimeter of two similar triangles ABC and PQR are 32cm and 24cm respectively. If PQ = 12cm, find AB. Sol: It is given that triangles ABC and PQR are similar. Therefore, Page 4 Exercise 4B 1. In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form: Sol: (i) We have: BAC = PQR = ABC = QPR = ACB = PRQ = QPR (ii) We have: But , EDF (Included angles are not equal) Thus, this triangles are not similar. (iii) We have: Also, ACB = PQR = - (iv) We have - (v) A + (Angle Sum Property) 2. BOC = 115 0 and CDO = 70 0 . Find (i) DCO (ii) DCO (iii) OAB (iv) OBA. Sol: (i) It is given that DB is a straight line. Therefore, (ii) Therefore, (iii) - Therefore, (iv) - Therefore, 3. If AB = 8cm, BO = 6.4cm, OC = 3.5cm and CD = 5cm, find (i) OA (ii) DO. Sol: (i) Let OA be X cm. - Hence, OA = 5.6 cm (ii) Let OD be Y cm - Hence, DO = 4 cm 4. In the given figure, if ADE = B, show that BE = 2.1cm and BC = 4.2cm, find DE. Sol: Given : Let DE be X cm - 5. The perimeter of two similar triangles ABC and PQR are 32cm and 24cm respectively. If PQ = 12cm, find AB. Sol: It is given that triangles ABC and PQR are similar. Therefore, 6. The corresponding sides of two similar triangles ABC and DEF are BC = 9.1cm and EF = Sol: - Therefore, their corresponding sides will be proportional. Also, the ratio of the perimeters of similar triangles is same as the ratio of their corresponding sides. m Therefore, 7. In the given figure, CAB = 90 0 and AD BC. AB = 1m and BC = 1.25m, find AD. Sol: - AD = = 0.6 m or 60 cm 8. In the given figure, ABC = 90 0 and BD AC. If AB = 5.7cm, BD = 3.8cm and CD = 5.4cm, find BC. Sol: It is given that ABC is a right angled triangle and BD is the altitude drawn from the right angle to the hypotenuse. Page 5 Exercise 4B 1. In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form: Sol: (i) We have: BAC = PQR = ABC = QPR = ACB = PRQ = QPR (ii) We have: But , EDF (Included angles are not equal) Thus, this triangles are not similar. (iii) We have: Also, ACB = PQR = - (iv) We have - (v) A + (Angle Sum Property) 2. BOC = 115 0 and CDO = 70 0 . Find (i) DCO (ii) DCO (iii) OAB (iv) OBA. Sol: (i) It is given that DB is a straight line. Therefore, (ii) Therefore, (iii) - Therefore, (iv) - Therefore, 3. If AB = 8cm, BO = 6.4cm, OC = 3.5cm and CD = 5cm, find (i) OA (ii) DO. Sol: (i) Let OA be X cm. - Hence, OA = 5.6 cm (ii) Let OD be Y cm - Hence, DO = 4 cm 4. In the given figure, if ADE = B, show that BE = 2.1cm and BC = 4.2cm, find DE. Sol: Given : Let DE be X cm - 5. The perimeter of two similar triangles ABC and PQR are 32cm and 24cm respectively. If PQ = 12cm, find AB. Sol: It is given that triangles ABC and PQR are similar. Therefore, 6. The corresponding sides of two similar triangles ABC and DEF are BC = 9.1cm and EF = Sol: - Therefore, their corresponding sides will be proportional. Also, the ratio of the perimeters of similar triangles is same as the ratio of their corresponding sides. m Therefore, 7. In the given figure, CAB = 90 0 and AD BC. AB = 1m and BC = 1.25m, find AD. Sol: - AD = = 0.6 m or 60 cm 8. In the given figure, ABC = 90 0 and BD AC. If AB = 5.7cm, BD = 3.8cm and CD = 5.4cm, find BC. Sol: It is given that ABC is a right angled triangle and BD is the altitude drawn from the right angle to the hypotenuse. By AA similarity theorem, we get : - Hence, BC = 8.1 cm 9. In the given figure, ABC = 90 0 and BD AC. If BD = 8cm, AD = 4cm, find CD. Sol: It is given that ABC is a right angled triangle and BD is the altitude drawn from the right angle to the hypotenuse. Therefore, by AA similarity theorem, we get : - CD = 10. P and Q are AQ = 3cm and QC = 6cm, show that BC = 3PQ. Sol: We have : Therefore, by AA similarity theorem, we get: - Hence, BC = 3PQRead More

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