Question

A transversal intersect two parallel lines. Prove that the bisector of any pair of corresponding angels so formed are parallel .

Answer 1

Given:

A transversal PQ cuts two lines AB and CD at E and F respectively.EG and FH are the bisectors of a pair of corresponding angles <PEB and

<EFD respectively such that EG||FH

To prove:

AB||CD

proof:-

EG||FH are cut by transversal EF

<PEG=<EFH {corresponding angle}

<GEB=<HFD

2<GEB=2<HFD

<PEB=<EFD {<GEB=1/2<PEB and <HFD=1/2<EFD}

But these corresponding angles when AB and CD are cut by the transversal PQ.

Therefore;

AB||CD {by corres. <s axiom}

Answer 2

Given: AB and CD are two straight lines cut by a transversal EF at G and H respectively. GM and HN are the bisectors of corresponding angles ∠EGB and ∠GHD respectively such that GM || HN

To prove - AB || HN

Proof:-

GM || HN

⇒∠1 = ∠2 (corresponding angle)

⇒2∠1 = 2∠2 ⇒∠EGB =∠GHD ⇒AB || CD

(∠EGB & ∠GHD are corresponding angles formed by transversal EF with AB and CD and are equal.)

Hence, proved.