Question

Three parallel lines p, q and r are intersected by two transversals l and m at A, B, C and D, E, F respectively
as shown in the figure.

$Prove \: that \: : \: \frac{AB}{BC} = \frac{DE}{EF} .$



No Spamming !



15❤ = 25❤ surely ! ​

Answer 1

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=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 △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.

Answer 2

Answer

Given = line P || line Q || line R

l and m are transversal line

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