Given:l∥m∥n l,m and n cut off equal intercepts AB and BC on p So,AB=BC To prove:l,m and n cut off equal intercepts DE and EF on q i.e.,DE=EF Proof:In △ACF, B is the mid-point of AC as AB=BC and BG∥CF since m∥n So,G is the mid-point of AF using line drawn throught mid-point of one side of a triangle, parallel to another side, bisects the third side. In △AFD, G is the mid-point of AF and GE∥AD since l∥m So,E is the mid-point of DF using line drawn throught mid-point of one side of a triangle, parallel to another side, bisects the third side. Since E is the mid-point of DF DE=EF Hence proved.