Example 8
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 . Show that l, m and n cut off equal intercepts DE and EF on q also.
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: Let us join A to F intersecting m at G..
In ACF,
B is the mid-point of AC
& BG CF
So, G is the mid-point of AF
In AFD,
G is the mid-point of AF
& GE AD
So, E is the mid-point of DF
Since E is the mid-point of DF,
DE = EF
Hence proved

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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