Question

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Question:
Draw the figure and then answer this question in your notebook.

Answer 1

Let the parallel lines l,m , n cut equal

intercepts AB and BC from the transversal

ABC .

Let DE , EF be the corresponding intercepts

cut from another transversal DEF .

It is required to prove that DE = EF

Through E draw a line MN parallel to

AC and touching the lines l and n.

Since l // m , and p // MN ,

therefore AMEB is a parallelogram--( 1 )

Similarly BENC is a parallelogram ---( 2 )

from ( 1 ) and ( 2 )

AB = ME ( opposite sides of parallelogram)

and ,

BC = EN

But AB = BC => ME = EN

In ∆'s DEM and NEF

EM = NE

<DEM = <NEF ( vertically opposite angles )

<DME = ENF ( alternate angles )

Therefore ,

∆DEM congruent to ∆NEF ( By ASA Rule )

Hence ,

DE = EF ( Corresponding parts of congruent

triangles )

I hope this helps you.

: )