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Construction 11.1 - Divide a line segment in a given ratio - Class 10

Construction 11.1 - Chapter 11 Class 10 Constructions - Part 2
Construction 11.1 - Chapter 11 Class 10 Constructions - Part 3 Construction 11.1 - Chapter 11 Class 10 Constructions - Part 4 Construction 11.1 - Chapter 11 Class 10 Constructions - Part 5

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Construction 11.1 To divide a line segment in a given ratio. Let us divide a line segment AB into 3:2 ratio. Steps of construction: Draw line segment AB Draw any ray AX, making an acute angle (angle less than 90Β°) with AB. Mark 5 (= 3 + 2) points 𝐴_1, 𝐴_2, 𝐴_3, 𝐴_4 and 𝐴_5 on AX, so that 〖𝐴𝐴〗_1=〖𝐴_1 𝐴〗_2=〖𝐴_2 𝐴〗_3=〖𝐴_3 𝐴〗_4=〖𝐴_4 𝐴〗_5 by drawing equal arcs Join 〖𝐡𝐴〗_5. Since we want the ratio 3 : 2, Through point 𝐴_3 (m = 3), we draw a line parallel to 𝐴_5 𝐡 by making ∠ AA5B = ∠ AA3C So, we copy ∠ AA5B from point A3 Thus, AC : CB = 3 : 2. Justification Since ∠ AA5B = ∠ AA3C, So, for lines A3C and A5B, with AX as transversal, corresponding angles are equal ∴ A3C is parallel to A5B Now, Since 𝐴_3 𝐢 is parallel to 𝐴_5 𝐡, 〖𝐴𝐴〗_3/(𝐴_3 𝐴_5 )=𝐴𝐢/𝐢𝐡 By construction, 〖𝐴𝐴〗_3/(𝐴_3 𝐴_5 )=3/2. Therefore, 𝐴𝐢/𝐢𝐡=3/2 Thus, C divides AB in the ratio 3 : 2.

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.