Question

(i) Prove that bisectors of any two opposite angles of a parallelogram are parallel.

Answer 1

Answer:

lets take PQRS 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

Answer 2

Answer :

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

Here, PQRS is a parallelogram and line segment PX,RY bisect angles P and R respectively.We have to prove that PX∥RY

Here, PQRS is a parallelogram and line segment PX,RY bisect angles P and R respectively.We have to prove that PX∥RYWe know that, in parallelogram opposite angles are equal.

∴ ∠P=∠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

Step-by-step explanation:

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