In parallelogram PQRS, O is the mid point of SQ. Find ∠S, ∠R, PQ, QR and diagonal PR.
Solution:
Given, PQRS is a parallelogram.
O is the midpoint of SQ
We have to find ∠S, ∠R, PQ, QR and diagonal PR.
Given, ∠RQY = 60°
Since SR || PY with RQ as transversal, the corresponding angles are equal.
∠SRQ = ∠RQY
So, ∠SRQ=60°
i.e., ∠R=60°
We know that the adjacent angles in a parallelogram are supplementary.
So, ∠PSR + ∠SRQ =180°
∠PSR + 60° = 180°
∠PSR = 180° - 60°
So, ∠PSR = 120°
i.e., ∠S = 120°
Given, SR = 15 cm
We know that the opposite sides of a parallelogram are equal.
So, SR = PQ
PQ = 15 cm
Similarly, PS = QR
QR = 11 cm
From the figure,
We observe that PR is bisected by SQ.
So, PR = 2 × PO
= 2 × 6
= 12 cm
Therefore, the diagonal PR is 12 cm.
✦ Try This: In Rhombus PQRS, O is the mid point of SQ. Find ∠S, ∠R, PQ, QR and diagonal PR
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 147
In parallelogram PQRS, O is the mid point of SQ. Find ∠S, ∠R, PQ, QR and diagonal PR.
Summary:
In parallelogram PQRS, O is the midpoint of SQ. The values of ∠S, ∠R, PQ, QR and diagonal PR are 120°, 60°, 15 cm, 11 cm and 12 cm.
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