Question

please answer my question
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Answer 1

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

Hope helps.......