Question

(1) Prove that bisectors of any two adjacent angles of a parallelogram are at right
angles.
ii) Prove that bisectors of any two opposite angles of a parallelogram are parallel.
ii) If the diagonals of a quadrilateral are equal and bisect each other at right angles,
then prove that it is a square.​

Answer 1

Answer:

ANSWER

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

⇒  21∠P=21∠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:

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