Question

if transvarsals two lines bisectors s​

Answer 1

Answer:

Step-by-step explanation:ANSWER

In figure, transversal AD intersects two lines PQ and RS at points B and C respectively.

Ray BE is the bisector of ∠ABQ

So, ∠ABE=∠EBQ=  

2

1

​  

(∠ABQ)  

and ray CG is the bisector of ∠BCS

So, ∠BCG=∠GCS=  

2

1

​  

(∠BCS)  

and BE∥CG

We should prove that PQ∥RS

Since, BE∥CG and line AD is the transversal,

∠ABE=∠BCG ------ Corresponding angles

2

1

​  

(∠ABQ)=  

2

1

​  

(∠BCS)

∠ABQ=∠BCS

But, these angles are the corresponding angles formed by transversal AD with PQ and RS

We know that, If a transversal intersects two lines such that the pair of corresponding angles is equal, then lines are parallel to each other.

So, PQ∥RS

Hence Proved.