Question

l, m and n are three parallel lines intersected by transversal p and q such that l, m and n cut equal intercepts ab and bc on p. show that l, m and n cuts off equal intercepts de and ef on q also

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

Answer 2

example no.3
hope it helps