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Is the given statement true or false?

In a rhombus PQRS, the diagonal PR bisects $∠ P$ as well as $∠ R$ .

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True

False

answer is A.

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Detailed Solution

It is given that,
In rhombus PQRS, diagonal PR bisects

as well as

.
Let us start by drawing a rhombus.
Question Image

PQRS is a rhombus, therefore

P Q = Q R = R S = P S

.
Also,

O P = O R

and

O Q = O S

.
In

Δ P O Q

and

Δ P O S

P Q = P S

… (From given)

P O = P O

… (Common side)
Also,

∠ P O Q = ∠ P O S = 90 °

∴ Δ A O B ≅ Δ A O D

… (By SSA congruence)
So.

∠ S P O = ∠ Q P O

, … (By CPCT) …(1)
Similarly, from

Δ R O S

and

Δ R O Q

, we can prove

∠ S R O = ∠ Q R O

. … (2)
Therefore, from (1) and (2) we can say in rhombus PQRS, the diagonal PR bisects

∠ P

as well as

∠ R

.
Hence, the given statement is true.
So, option 1 is the correct choice.

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