Advertisements
Advertisements
Question
In parallelogram PQRS, O is the mid point of SQ. Find ∠S, ∠R, PQ, QR and diagonal PR.
Advertisements
Solution
Given, ∠RQY = 60°
∴ ∠RQP = 120° ...[Linear pair]
∴ ∠S = 120° ...[∵ Opposite angles are equal in a parallelogram]
By the angle sum property of a quadrilateral,
∠P + ∠R + ∠S + ∠Q = 360°
⇒ ∠P + ∠R + 120° + 120° = 360°
⇒ ∠P + ∠R + 120°
⇒ 2∠P = 120°
⇒ ∠P = 60° ...[∵ Opposite angles are equal in parallelogram]
⇒ ∠P = ∠R = 60°
Also, SR = 15 cm
∴ PQ = 15 cm ...[∵ Opposite sides of a parallelogram are equal]
And PS = 11 cm
∴ QR = 11 cm ...[∵ Opposite sides of a parallelogram are equal]
And PR = 2 × PO
= 2 × 6
= 12 cm ...[∵ Diagonals of a parallelogram bisect each other]
APPEARS IN
RELATED QUESTIONS
Given a parallelogram ABCD. Complete each statement along with the definition or property used.
- AD = ______
- ∠DCB = ______
- OC = ______
- m∠DAB + m∠CDA = ______
Consider the given parallelograms. Find the values of the unknowns x, y, z.
The following figure GUNS is a parallelogram. Find x and y. (Lengths are in cm)
In the above figure both RISK and CLUE are parallelograms. Find the value of x.
Find the measure of ∠P and ∠S, if `bar(SP) || bar(RQ)` in the following figure. (If you find m∠R, is there more than one method to find m∠P?).
In the given figure, if points P, Q, R, S are on the sides of parallelogram such that AP = BQ = CR = DS then prove that `square`PQRS is a parallelogram.
The angle between the two altitudes of a parallelogram through the same vertex of an obtuse angle of the parallelogram is 30°. The measure of the obtuse angle is ______.
Find the values of x and y in the following parallelogram.
A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.
The following figure RUNS is parallelogram. Find x and y. (Lengths are in cm)
