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
Can a quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180°?
In the above figure both RISK and CLUE are parallelograms. Find the value of x.
In the given figure, `square`ABCD is a parallelogram. Point E is on the ray AB such that BE = AB then prove that line ED bisects seg BC at point F.
Ratio of two adjacent sides of a parallelogram is 3 : 4, and its perimeter is 112 cm. Find the length of its each side.
In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.
In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD. Prove that:
- AE = AD,
- DE bisects and ∠ADC and
- Angle DEC is a right angle.
Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between b and c
Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between d and f
Which of the following figures satisfy the following properties?
- All sides are congruent.
- All angles are right angles.
- Opposite sides are parallel.
ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is AXCY a parallelogram? Give reason.
