Constructions
Concept wise

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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.