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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 π΄_1, π΄_2, π΄_3, π΄_4 and π΄_5 on AX, so that γπ΄π΄γ_1=γπ΄_1 π΄γ_2=γπ΄_2 π΄γ_3=γπ΄_3 π΄γ_4=γπ΄_4 π΄γ_5 by drawing equal arcs Join γπ΅π΄γ_5. Since we want the ratio 3 : 2, Through point π΄_3 (m = 3), we draw a line parallel to π΄_5 π΅ by making β  AA5B = β  AA3C So, we copy β  AA5B from point A3 Thus, AC : CB = 3 : 2. Justification Since β  AA5B = β  AA3C, So, for lines A3C and A5B, with AX as transversal, corresponding angles are equal β΄ A3C is parallel to A5B Now, Since π΄_3 πΆ is parallel to π΄_5 π΅, γπ΄π΄γ_3/(π΄_3 π΄_5 )=π΄πΆ/πΆπ΅ By construction, γπ΄π΄γ_3/(π΄_3 π΄_5 )=3/2. Therefore, π΄πΆ/πΆπ΅=3/2 Thus, C divides AB in the ratio 3 : 2.

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.