Question

prove that intersept theorm​

Answer 1

Answer:

Statement: If there are three or more parallel lines and the intercepts made by them on one transversal are equal, the corresponding intercepts of any transversal are also equal.

Given: l||m||n

P is a transversal intersecting l, m and n at A, B and C respectively such that AB=BC.

Q is another transversal drawn to cut l, m and n at D, E and F respectively. DE and EF are the intercepts made on q.

To prove: DE = EF

Construction: Draw a line through E parallel to p intersecting l in G, n in H respectively.

Proof: AG||BE (given) GE||AB (by construction) AGEB is a parallelogram

From (i) and (ii), GE=EH

Now compare triangles GED and EFH,

GE=EH (proved)

Hence the theorem is proved.

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