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प्रश्न
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
विकल्प
True
False
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).
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संबंधित प्रश्न
Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
ABCD is a parallelogram. What kind of quadrilateral is it if : AC = BD and AC is perpendicular to BD?
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.
In the given figure, AB || EC, AB = AC and AE bisects ∠DAC. Prove that:
- ∠EAC = ∠ACB
- ABCE is a parallelogram.
Which of the following is a property of a parallelogram?
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.
Construct a parallelogram when one of its side is 4 cm and its two diagonals are 5.6 cm and 7 cm. Measure the other side.
The following figure RUNS is parallelogram. Find x and y. (Lengths are in cm)
