Question

l parallel to m parallel to n. p and q are 2 transversal such that l,m,n cut off equal intercepts AB and Bc on line p.proove that the interspts DE and EF are also equal.​

Answer 1

Answer:

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 △ACF,

• B is the mid-point of AC as AB=BCand 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 △AFD,

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

Hence proved.