Question

Prove that bisectors of any two opposite angles of a parallelogram are parallel.​

Answer 1

Answer:

Step-by-step explanation:

Here, PQRS is a parallelogram and line segment  PX,RY bisect angles P and R respectively.

We have to prove that PX∥RY

We know that, in parallelogram opposite angles are equal.

∴  ∠P=∠R

⇒    

2

1

​  

∠P=  

2

1

​  

∠R

⇒  ∠1=∠2           ---- ( 1 )  [ Since, PX and RY are bisectors of ∠P and ∠R respectively ]

Now, PQ∥RS and the transversal RY intersects them.

∴  ∠2=∠3        ---- ( 2 )   [ Alternate angles ]

From ( 1 ) and ( 2 ) we get,

⇒  ∠1=∠3

Thus, transversal PQ intersects PX and YR at P and Y such that ∠1=∠3 i.e. corresponding angles are equal.

∴  PX∥RY