Advertisements
Advertisements
प्रश्न
PQRS is a quadrilateral, PR and QS intersect each other at O. In which of the following case, PQRS is a parallelogram?
∠P = 100°, ∠Q = 80°, ∠R = 95°
Advertisements
उत्तर
We have a quadrilateral named PQRS, with diagonals PR and QS intersecting at O.
∠P =100° , ∠Q = 80° ,∠R = 100°
By angle sum property of a quadrilateral, we get:
∠P + ∠Q + ∠R +∠S = 360°
100° + 80° + 100° +∠S = 360°
280° +∠S 360°
∠S = 80°
Clearly, ∠P = ∠R
And ∠Q = ∠S
Thus we have PQRS a quadrilateral with opposite angles are equal.
Therefore,
PQRS is a parallelogram.
APPEARS IN
संबंधित प्रश्न
In Fig., below, ABCD is a parallelogram in which ∠A = 60°. If the bisectors of ∠A and ∠B meet at P, prove that AD = DP, PC = BC and DC = 2AD.
In a parallelogram ABCD, determine the sum of angles ∠C and ∠D .
In a parallelogram ABCD, if `∠`B = 135°, determine the measures of its other angles .
P and Q are the points of trisection of the diagonal BD of a parallelogram AB Prove that CQ is parallel to AP. Prove also that AC bisects PQ.
In a ΔABC median AD is produced to X such that AD = DX. Prove that ABXC is a
parallelogram.
In Fig. below, AB = AC and CP || BA and AP is the bisector of exterior ∠CAD of ΔABC.
Prove that (i) ∠PAC = ∠BCA (ii) ABCP is a parallelogram
In a parallelogram ABCD, write the sum of angles A and B.
We get a rhombus by joining the mid-points of the sides of a
The figure formed by joining the mid-points of the adjacent sides of a parallelogram is a
ABCD is a square, diagonals AC and BD meet at O. The number of pairs of congruent triangles with vertex O are
