1. Chapter 11 Class 10 Constructions
  2. Serial order wise
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Ex 11.1, 1 Draw a line segment length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts. Give the justification of the construction. Steps of construction: Draw line AB of length 7.6 cm Draw any ray AX, making an acute angle (angle less than 90°) with AB. Mark 13 (= 5 + 8) points, A_1, (A)_2,  A_3,  A_4……. A_13, on AX such that (AA)_1=A_1 A_2=A_2 A_3 and so on. Join (BA)_13. Since we want the ratio 5 : 8, Through point A_5 (m = 5), we draw a line parallel to (BA)_13(by making an angle equal to ∠AA13B at A5) intersecting AB at the point C. Then, AC : CB = 5 : 8. Measuring by scale, AC = 2.9 cm and BC = 4.7 cm Justification In Δ AA13B Since A_3 C is parallel to A_5 B, therefore,   (AA)_5/(A_5 A_13 )=AC/CB By construction, (AA)_3/(A_3 A_5 )=5/8. Therefore, AC/CB=5/8. This shows that C divides AB in the ratio 5 : 8.

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.