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opaallelogram.t, m and n are three parallel lines intersected by transversal p and q suchthat I, m and n cut off equal intercepts AB and BC on p. Show that I, m andn cut off equal intercepts DE and Ef on g also |
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Answer» Let l, m and n be three parallel lines intersected by two transversals p and q such that l, m and n cut off equal intercepts AB and BC on p i.e. AB = BC. To show: l, m and n cut off equal intercepts DE and EF on q also, i.e. DE = EF. Construction: Join AF intersecting m at G. So, the trapezium ACFD is divided into two triangles: ΔACF and ΔAFD. It is given that AB = BC ⇒ B is the mid point of AC Now in ΔACF, B is the mid point of AC and BG || CF(as m || n ) ∴ By mid point theorem, G is the mid point of AF. Now in ΔAFD, G is the mid point of AF and GE || AD(as l || m) ⇒ E is the mid point of DF (by mid point theorem) ⇒ DE = EF hit like if you find it useful |
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