Advertisements
Advertisements
प्रश्न
In quadrilateral PQRS, ∠P : ∠Q : ∠R : ∠S = 3 : 4 : 6 : 7.
Calculate each angle of the quadrilateral and then prove that PQ and SR are parallel to each other
(i) Is PS also parallel to QR?
(ii) Assign a special name to quadrilateral PQRS.
Advertisements
उत्तर
∵ ∠P : ∠Q : ∠R : ∠S = 3: 4: 6: 7
Let ∠P = 3x
∠Q = 4x
∠R = 6x
∠S = 7x
∴ ∠P + ∠Q + ∠R + ∠S = 360°
3x + 4x + 6x + 7x = 360°
20x = 360°
x = 18°
∴ ∠P = 3x = 3 × 18 = 54°
∠Q = 4x = 4 × 18 = 72°
∠R = 6x = 6 × 18 = 108°
∠S = 7x = 7 × 18 = 126°
∠Q + ∠R = 72° + 108° = 180°
or ∠P + ∠S = 54° + 126° = 180°
Hence PQ || SR
As ∠P + ∠Q = 72° + 54° = 126°
Which is ≠ 180°
∴ PS and QR are not parallel.
PQRS is a Trapezium as its one pair of opposite side is parallel.
संबंधित प्रश्न
In a quadrilateral, define of the following Sides.
The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sided of the polygon.
Complete the following statement by means of one of those given in brackets against each:
If one pair of opposite sides are equal and parallel, then the figure is ........................
Complete the following statement by means of one of those given in brackets against each:
A line drawn from the mid-point of one side of a triangle .............. another side intersects the third side at its mid-point.
Complete the following statement by means of one of those given in brackets against each:
If both pairs of opposite sides of a quadrilateral are equal, then it is necessarily a ...............
If the bisectors of two adjacent angles A and B of a quadrilateral ABCD intersect at a point O such that ∠C + ∠D = k ∠AOB, then find the value of k.
Angles of a quadrilateral are (4x)°, 5(x+2)°, (7x – 20)° and 6(x+3)°. Find :
(i) the value of x.
(ii) each angle of the quadrilateral.
Given : In quadrilateral ABCD ; ∠C = 64°, ∠D = ∠C – 8° ; ∠A = 5(a+2)° and ∠B = 2(2a+7)°.
Calculate ∠A.
In a quadrilateral ABCD, AO and BO are bisectors of angle A and angle B respectively. Show that:
∠AOB = (∠C + ∠D)
The angles A, B, C and D of a quadrilateral are in the ratio 2 : 3 : 2 : 3. Show this quadrilateral is a parallelogram.
Calculate the measure of each angle of a nonagon.
ΔPQR and ΔSQR are on the same base QR with P and S on opposite sides of line QR, such that area of ΔPQR is equal to the area of ΔSQR. Show that QR bisects PS.
In quadrilateral HOPE, the pairs of opposite sides are ______.
In quadrilateral WXYZ, the pairs of opposite angles are ______.
The diagonals of the quadrilateral DEFG are ______ and ______.
Using the information given, name the right angles in part of figure:
AE ⊥ CE
What conclusion can be drawn from part of given figure, if DB is the bisector of ∠ADC?
Draw a rough sketch of a quadrilateral KLMN. State two pairs of opposite angles.
Investigate :
Use strips and fasteners to make a triangle and a quadrilateral.
Try to push inward at any one vertex of the triangle. Do the same to the quadrilateral. Is the triangle distorted? Is the quadrilateral distorted? Is the triangle rigid?
Why is it that structures like electric towers make use of triangular shapes and not quadrilaterals?
How many points are required to form a quadrilateral?
