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Condition for Two Lines to Be Parallel

Which of the ...

Question

Which of the following statements is definitely true, if PQRS is a parallelogram?

P Q

and

S R

are adjacent sides.

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∠ P

and

∠ Q

are opposite angles

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S R ∥ P Q

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P R = R Q

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Solution

The correct option is C $S R ∥ P Q$
Given PQRS is a parallelogram.
$2$ options are possible as given in figure.
Option A: PQ and SR may or may not be adjacent sides.
Option B: Angle P and Q are adjacent angles as they lie on same edge.
Option C: SR is parallel to PQ in either case.
Option D: PR is not equal to RQ as one of them is side and other is diagnol.

Option C is correct.

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Similar questions

In a quadrilateral PQRS, opposite angles are equal. If SR = 2 cm and PR = 5 cm then determine PQ.

A B C D

P, Q, R

S

A B, B C, C D

D A . A C

S R ∥ A C

S R = \frac{1}{2} A C

P Q = S R

P Q R S

The diagonal PR of a quadrilateral PQRS bisects the angles P and R, then

A B C D

P, Q, R

S

A B, B C, C D

D A

A C

S R ∥ A C

S R = \frac{1}{2} A C

P Q = S R

P Q R S

P. Q, R and S are respectively the midpoints of the sides AB, BC, CD and DA of a quadrilateral ABCD. Show that

(i) PQ || AC and $P Q = \frac{1}{2} A C$

(ii) PQ || SR

(iii) PQRS is a parallelogram.

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