l, m and n are three parallel lines intersected by transversals p and q such that l, m and n cut off equal intercepts AB and BC on p (see Fig.). Show that l, m and n cut off equal intercepts DE and EF on q also

Explanation

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 `triangleACF`,
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 `triangleAFD`,
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`
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