Page 1 1. Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that 3 5 AP AB . Sol: Steps of Construction: Step 1: Draw a line segment 7 A B c m Step 2: Draw a ray A X, making an acute angle . BA X Step 3: Along A X, mark 5 points (greater of 3 and 5) 1 2 3 4 , , , A A A A and 5 A such that 1 1 2 2 3 3 4 4 5 A A A A A A A A A A Step 4: Join 5 . A B Step 5: From 3 , A draw 3 A P parallel to 5 A B (draw an angle equal to 5 AA B ), meeting A B in P. Here, P is the point on AB such that 3 2 A P P B or 3 . 5 A P A B 2. Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Sol: Steps of Construction: Step 1: Draw a line segment 7.6 A B c m Step 2: Draw a ray A X, making an acute angle . BA X Step 3: Along A X, mark 5 8 13points 1 2 3 4 5 6 7 8 9 10 11 12 , , , , , , , , , , , A A A A A A A A A A A A and 13 A such that 1 1 2 2 3 3 4 4 5 6 7 8 9 9 10 10 11 11 12 12 13 . A A A A A A A A A A A A A A A A A A A A A A Step 4: Join 13 . A B Step 5: From 5 , A draw 5 A P parallel to 13 A B (draw an angle equal to 13 A A B ), meeting A B in P. Page 2 1. Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that 3 5 AP AB . Sol: Steps of Construction: Step 1: Draw a line segment 7 A B c m Step 2: Draw a ray A X, making an acute angle . BA X Step 3: Along A X, mark 5 points (greater of 3 and 5) 1 2 3 4 , , , A A A A and 5 A such that 1 1 2 2 3 3 4 4 5 A A A A A A A A A A Step 4: Join 5 . A B Step 5: From 3 , A draw 3 A P parallel to 5 A B (draw an angle equal to 5 AA B ), meeting A B in P. Here, P is the point on AB such that 3 2 A P P B or 3 . 5 A P A B 2. Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Sol: Steps of Construction: Step 1: Draw a line segment 7.6 A B c m Step 2: Draw a ray A X, making an acute angle . BA X Step 3: Along A X, mark 5 8 13points 1 2 3 4 5 6 7 8 9 10 11 12 , , , , , , , , , , , A A A A A A A A A A A A and 13 A such that 1 1 2 2 3 3 4 4 5 6 7 8 9 9 10 10 11 11 12 12 13 . A A A A A A A A A A A A A A A A A A A A A A Step 4: Join 13 . A B Step 5: From 5 , A draw 5 A P parallel to 13 A B (draw an angle equal to 13 A A B ), meeting A B in P. Here, P is the point on A B which divides it in the ratio 5 :8. Length of 2.9 AP c m (Approx) Length of 4.7 B P c m (Approx) 3. Construct a P Q R , in which PQ = 6 cm, QR = 7 cm and PR =- 8 cm. Then, construct another triangle whose sides are 4 5 times the corresponding sides of P Q R Sol: Steps of Construction Step 1: Draw a line segment 7 . Q R c m Step 2: With Q as center and radius 6 cm, draw an arc. Step 3: With R as center and radius 8cm, draw an arc cutting the previous arc at P Step 4: Join P Q and P R . Thus, P Q R is the required triangle. Step 5: Below QR, draw an acute angle . R Q X Step 6: Along OX, mark five points 1 2 3 4 , , , R R R R and 5 R such that 1 1 2 2 3 3 4 4 5 . Q R R R R R R R R R Step 7: Join 5 . R R Step 8: From 4 , R draw 4 5 '|| R R R R meeting Q R at R Step 9: From R P R P R meeting P Q . Page 3 1. Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that 3 5 AP AB . Sol: Steps of Construction: Step 1: Draw a line segment 7 A B c m Step 2: Draw a ray A X, making an acute angle . BA X Step 3: Along A X, mark 5 points (greater of 3 and 5) 1 2 3 4 , , , A A A A and 5 A such that 1 1 2 2 3 3 4 4 5 A A A A A A A A A A Step 4: Join 5 . A B Step 5: From 3 , A draw 3 A P parallel to 5 A B (draw an angle equal to 5 AA B ), meeting A B in P. Here, P is the point on AB such that 3 2 A P P B or 3 . 5 A P A B 2. Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Sol: Steps of Construction: Step 1: Draw a line segment 7.6 A B c m Step 2: Draw a ray A X, making an acute angle . BA X Step 3: Along A X, mark 5 8 13points 1 2 3 4 5 6 7 8 9 10 11 12 , , , , , , , , , , , A A A A A A A A A A A A and 13 A such that 1 1 2 2 3 3 4 4 5 6 7 8 9 9 10 10 11 11 12 12 13 . A A A A A A A A A A A A A A A A A A A A A A Step 4: Join 13 . A B Step 5: From 5 , A draw 5 A P parallel to 13 A B (draw an angle equal to 13 A A B ), meeting A B in P. Here, P is the point on A B which divides it in the ratio 5 :8. Length of 2.9 AP c m (Approx) Length of 4.7 B P c m (Approx) 3. Construct a P Q R , in which PQ = 6 cm, QR = 7 cm and PR =- 8 cm. Then, construct another triangle whose sides are 4 5 times the corresponding sides of P Q R Sol: Steps of Construction Step 1: Draw a line segment 7 . Q R c m Step 2: With Q as center and radius 6 cm, draw an arc. Step 3: With R as center and radius 8cm, draw an arc cutting the previous arc at P Step 4: Join P Q and P R . Thus, P Q R is the required triangle. Step 5: Below QR, draw an acute angle . R Q X Step 6: Along OX, mark five points 1 2 3 4 , , , R R R R and 5 R such that 1 1 2 2 3 3 4 4 5 . Q R R R R R R R R R Step 7: Join 5 . R R Step 8: From 4 , R draw 4 5 '|| R R R R meeting Q R at R Step 9: From R P R P R meeting P Q . Here, ' ' P Q R is the required triangle, each of whose sides are 4 5 times the corresponding sides of . P Q R 4. Construct a triangle with sides 5 cm, 6 cm, and 7 cm and then another triangle whose sides are 7 5 of the corresponding sides of the first triangle. Sol: Steps of Construction : Step 1: Draw a line segment 4 . BC c m Step 2: With B as center, draw an angle of 90 . Step 3: With B as center and radius equal to 3 cm, cut an arc at the right angle and name it A. Step 4: Join A B and A C. Thus, ABC is obtained. Step 5: Extend B C to D, such that 7 75 4 5.6 . 5 B D B C c m c m Step 6: Draw || , D E C A cutting AB produced to E. Thus, E B D is the required triangle, each of whose sides is 7 5 the corresponding sides of . A B C 5. Construct a A B C with BC = 7 cm, 60 B and AB = 6 cm. Construct another triangle whose sides are 3 4 times the corresponding sides of A B C Sol: Steps of Construction Step 1: Draw a line segment 7 . BC c m Step 2: At B, draw 60 . XBC Step 3: With B as center and radius 6 cm, draw an arc cutting the ray B X at A. Step 4: Join A C. Thus, A B C is the required triangle. Step 5: Below B C, draw an acute angle . Y B C Step 6: Along B Y, mark four points 1 2 3 , , B B B and 4 B such that 1 1 2 2 3 3 4 . B B B B B B B B Page 4 1. Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that 3 5 AP AB . Sol: Steps of Construction: Step 1: Draw a line segment 7 A B c m Step 2: Draw a ray A X, making an acute angle . BA X Step 3: Along A X, mark 5 points (greater of 3 and 5) 1 2 3 4 , , , A A A A and 5 A such that 1 1 2 2 3 3 4 4 5 A A A A A A A A A A Step 4: Join 5 . A B Step 5: From 3 , A draw 3 A P parallel to 5 A B (draw an angle equal to 5 AA B ), meeting A B in P. Here, P is the point on AB such that 3 2 A P P B or 3 . 5 A P A B 2. Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Sol: Steps of Construction: Step 1: Draw a line segment 7.6 A B c m Step 2: Draw a ray A X, making an acute angle . BA X Step 3: Along A X, mark 5 8 13points 1 2 3 4 5 6 7 8 9 10 11 12 , , , , , , , , , , , A A A A A A A A A A A A and 13 A such that 1 1 2 2 3 3 4 4 5 6 7 8 9 9 10 10 11 11 12 12 13 . A A A A A A A A A A A A A A A A A A A A A A Step 4: Join 13 . A B Step 5: From 5 , A draw 5 A P parallel to 13 A B (draw an angle equal to 13 A A B ), meeting A B in P. Here, P is the point on A B which divides it in the ratio 5 :8. Length of 2.9 AP c m (Approx) Length of 4.7 B P c m (Approx) 3. Construct a P Q R , in which PQ = 6 cm, QR = 7 cm and PR =- 8 cm. Then, construct another triangle whose sides are 4 5 times the corresponding sides of P Q R Sol: Steps of Construction Step 1: Draw a line segment 7 . Q R c m Step 2: With Q as center and radius 6 cm, draw an arc. Step 3: With R as center and radius 8cm, draw an arc cutting the previous arc at P Step 4: Join P Q and P R . Thus, P Q R is the required triangle. Step 5: Below QR, draw an acute angle . R Q X Step 6: Along OX, mark five points 1 2 3 4 , , , R R R R and 5 R such that 1 1 2 2 3 3 4 4 5 . Q R R R R R R R R R Step 7: Join 5 . R R Step 8: From 4 , R draw 4 5 '|| R R R R meeting Q R at R Step 9: From R P R P R meeting P Q . Here, ' ' P Q R is the required triangle, each of whose sides are 4 5 times the corresponding sides of . P Q R 4. Construct a triangle with sides 5 cm, 6 cm, and 7 cm and then another triangle whose sides are 7 5 of the corresponding sides of the first triangle. Sol: Steps of Construction : Step 1: Draw a line segment 4 . BC c m Step 2: With B as center, draw an angle of 90 . Step 3: With B as center and radius equal to 3 cm, cut an arc at the right angle and name it A. Step 4: Join A B and A C. Thus, ABC is obtained. Step 5: Extend B C to D, such that 7 75 4 5.6 . 5 B D B C c m c m Step 6: Draw || , D E C A cutting AB produced to E. Thus, E B D is the required triangle, each of whose sides is 7 5 the corresponding sides of . A B C 5. Construct a A B C with BC = 7 cm, 60 B and AB = 6 cm. Construct another triangle whose sides are 3 4 times the corresponding sides of A B C Sol: Steps of Construction Step 1: Draw a line segment 7 . BC c m Step 2: At B, draw 60 . XBC Step 3: With B as center and radius 6 cm, draw an arc cutting the ray B X at A. Step 4: Join A C. Thus, A B C is the required triangle. Step 5: Below B C, draw an acute angle . Y B C Step 6: Along B Y, mark four points 1 2 3 , , B B B and 4 B such that 1 1 2 2 3 3 4 . B B B B B B B B Step 7: Join 4 . C B Step 8: From 3 , B draw 3 4 '|| B C C B meeting B C at ' C ' '|| A C A C meeting A B Here. ' ' A B C is the required triangle whose sides are 3 4 times the corresponding sides of . A B C 6. Construct a A B C in which AB = 6 cm, 30 A and 60 A B . Construct another ' ' A B C similar to A B C Sol: Steps of Construction Step 1: Draw a line segment 6 . AB c m Step 2: At A, draw 30 . XA B Step 3: At B, draw 60 . Y BA Suppose AX and BY intersect at C. Thus, A B C is the required triangle. Step 4: Produce AB to B such that ' 8 . AB c m ' '|| B C B C . A B C 7. Construct a A B C in which BC = 8 cm, 45 B and 60 C . Construct another triangle similar to A B C such that its sides are 3 5 of the corresponding sides of A B C . Sol: Steps of Construction Step 1: Draw a line segment 8 . B C c m Step 2: At B, draw 45 . XBC Page 5 1. Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that 3 5 AP AB . Sol: Steps of Construction: Step 1: Draw a line segment 7 A B c m Step 2: Draw a ray A X, making an acute angle . BA X Step 3: Along A X, mark 5 points (greater of 3 and 5) 1 2 3 4 , , , A A A A and 5 A such that 1 1 2 2 3 3 4 4 5 A A A A A A A A A A Step 4: Join 5 . A B Step 5: From 3 , A draw 3 A P parallel to 5 A B (draw an angle equal to 5 AA B ), meeting A B in P. Here, P is the point on AB such that 3 2 A P P B or 3 . 5 A P A B 2. Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts. Sol: Steps of Construction: Step 1: Draw a line segment 7.6 A B c m Step 2: Draw a ray A X, making an acute angle . BA X Step 3: Along A X, mark 5 8 13points 1 2 3 4 5 6 7 8 9 10 11 12 , , , , , , , , , , , A A A A A A A A A A A A and 13 A such that 1 1 2 2 3 3 4 4 5 6 7 8 9 9 10 10 11 11 12 12 13 . A A A A A A A A A A A A A A A A A A A A A A Step 4: Join 13 . A B Step 5: From 5 , A draw 5 A P parallel to 13 A B (draw an angle equal to 13 A A B ), meeting A B in P. Here, P is the point on A B which divides it in the ratio 5 :8. Length of 2.9 AP c m (Approx) Length of 4.7 B P c m (Approx) 3. Construct a P Q R , in which PQ = 6 cm, QR = 7 cm and PR =- 8 cm. Then, construct another triangle whose sides are 4 5 times the corresponding sides of P Q R Sol: Steps of Construction Step 1: Draw a line segment 7 . Q R c m Step 2: With Q as center and radius 6 cm, draw an arc. Step 3: With R as center and radius 8cm, draw an arc cutting the previous arc at P Step 4: Join P Q and P R . Thus, P Q R is the required triangle. Step 5: Below QR, draw an acute angle . R Q X Step 6: Along OX, mark five points 1 2 3 4 , , , R R R R and 5 R such that 1 1 2 2 3 3 4 4 5 . Q R R R R R R R R R Step 7: Join 5 . R R Step 8: From 4 , R draw 4 5 '|| R R R R meeting Q R at R Step 9: From R P R P R meeting P Q . Here, ' ' P Q R is the required triangle, each of whose sides are 4 5 times the corresponding sides of . P Q R 4. Construct a triangle with sides 5 cm, 6 cm, and 7 cm and then another triangle whose sides are 7 5 of the corresponding sides of the first triangle. Sol: Steps of Construction : Step 1: Draw a line segment 4 . BC c m Step 2: With B as center, draw an angle of 90 . Step 3: With B as center and radius equal to 3 cm, cut an arc at the right angle and name it A. Step 4: Join A B and A C. Thus, ABC is obtained. Step 5: Extend B C to D, such that 7 75 4 5.6 . 5 B D B C c m c m Step 6: Draw || , D E C A cutting AB produced to E. Thus, E B D is the required triangle, each of whose sides is 7 5 the corresponding sides of . A B C 5. Construct a A B C with BC = 7 cm, 60 B and AB = 6 cm. Construct another triangle whose sides are 3 4 times the corresponding sides of A B C Sol: Steps of Construction Step 1: Draw a line segment 7 . BC c m Step 2: At B, draw 60 . XBC Step 3: With B as center and radius 6 cm, draw an arc cutting the ray B X at A. Step 4: Join A C. Thus, A B C is the required triangle. Step 5: Below B C, draw an acute angle . Y B C Step 6: Along B Y, mark four points 1 2 3 , , B B B and 4 B such that 1 1 2 2 3 3 4 . B B B B B B B B Step 7: Join 4 . C B Step 8: From 3 , B draw 3 4 '|| B C C B meeting B C at ' C ' '|| A C A C meeting A B Here. ' ' A B C is the required triangle whose sides are 3 4 times the corresponding sides of . A B C 6. Construct a A B C in which AB = 6 cm, 30 A and 60 A B . Construct another ' ' A B C similar to A B C Sol: Steps of Construction Step 1: Draw a line segment 6 . AB c m Step 2: At A, draw 30 . XA B Step 3: At B, draw 60 . Y BA Suppose AX and BY intersect at C. Thus, A B C is the required triangle. Step 4: Produce AB to B such that ' 8 . AB c m ' '|| B C B C . A B C 7. Construct a A B C in which BC = 8 cm, 45 B and 60 C . Construct another triangle similar to A B C such that its sides are 3 5 of the corresponding sides of A B C . Sol: Steps of Construction Step 1: Draw a line segment 8 . B C c m Step 2: At B, draw 45 . XBC Step 3: At C, draw 60 . Y C B Suppose B X and C Y intersect at A. Thus, A B C is the required triangle Step 4: Below B C, draw an acute angle . Z B C Step 5: Along B Z, mark five points 1 2 3 4 5 , , , Z Z Z Z a n d Z such that 1 1 2 2 3 3 4 4 5. B Z Z Z Z Z Z Z Z Z Step 6: Join 5 . C Z Step 7: From 3 , Z draw 3 5 '|| Z C C Z meeting B C Step 8: From C ' '|| A C A C meeting AB Here, ' ' A B C is the required triangle whose sides are 3 5 of the corresponding sides of . A B C 8. To construct a triangle similar to A B C in which BC = 4.5 cm, 45 B and 60 C , using a scale factor of 3 7 , BC will be divided in the ratio (a) 3 : 4 (b) 4 : 7 (c) 3 : 10 (d) 3 : 7 Answer: (a) 3 : 4 Sol: To construct a triangle similar to A B C in which 4.5 , 45 60 , B C c m B a n d C using a scale factor of 3 , 7 B C will be divided in the ratio 3: 4. Here, ~ ' ' AB C A BC ': ' 3: 4 BC C C or ': 3: 7 BC BC Hence, the correct answer is option A.Read More

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