Advertisements
Advertisements
प्रश्न
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
पर्याय
True
False
Advertisements
उत्तर
This statement is True.
Explanation:
⇒ Let ABCD be a parallelogram, with A = α and B = β.
We have to prove that C = α and D = β.
⇒ α + β = 180° (co-interior angles, AD || BC),
⇒ ∠C = α (co-interior angles, AB || DC)
⇒ ∠D = β (co-interior angles, AB || DC).
APPEARS IN
संबंधित प्रश्न
The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.
Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
In the above figure both RISK and CLUE are parallelograms. Find the value of x.
Name the quadrilaterals whose diagonals bisect each other
Perimeter of a parallelogram is 150 cm. One of its sides is greater than the other side by 25 cm. Find the lengths of all sides.
PQRS is a parallelogram whose diagonals intersect at M.
If ∠PMS = 54°, ∠QSR = 25° and ∠SQR = 30° ; find :
(i) ∠RPS
(ii) ∠PRS
(iii) ∠PSR.
ABCD is a parallelogram. What kind of quadrilateral is it if: AC = BD but AC is not perpendicular to BD?
In the following diagram, the bisectors of interior angles of the parallelogram PQRS enclose a quadrilateral ABCD.
Show that:
(i) ∠PSB + ∠SPB = 90°
(ii) ∠PBS = 90°
(iii) ∠ABC = 90°
(iv) ∠ADC = 90°
(v) ∠A = 90°
(vi) ABCD is a rectangle
Thus, the bisectors of the angles of a parallelogram enclose a rectangle.
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 ______.
The adjacent sides of a parallelogram are 5 cm and 9 cm. Its perimeter is ______.
