Question

if
a transversal intersects two lines such that the
bisectors of a pair of alternate interior angles are
parallel, then prove that the two lines are parallel​

Answer 1

AnswEr :

It is given that,

• A transversal AD intersects the 2 lines PQ and RS at points B and C respectively !

✩ CF is the bisector of ∠BCS

✩ BE is the bisector of ∠ABQ

So,

➝ ∠ABE= ½∠ABQ

➝ ∠BCF = ½∠BCS

Also, from the figure we can say that,

• BE and CF are parallel to each other.

• AD is the transversal

So by Corresponding Angle axiom,

➝ ∠ABE =∠BCF

➝ ∠ABQ= ½∠BCS

Hence,

➝ ∠ABQ=∠BCS

$\therefore$ PQ is parallel to RS.

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✩ Know More about the topic :

Corresponding angle axiom states that,

If a transversal intersects any 2 parallel lines, then each pair of corresponding angles are said to be equal .

Opposite / Converse axiom :

If a transversal intersects any 2 parallel lines such that a pair of corresponding angles is equal then the 2 lines are said to be parallel.

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