Advertisements
Advertisements
Question
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
Options
True
False
Solution
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
RELATED QUESTIONS
Given a parallelogram ABCD. Complete each statement along with the definition or property used.
- AD = ______
- ∠DCB = ______
- OC = ______
- m∠DAB + m∠CDA = ______
Can a quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180°?
The following figure GUNS is a parallelogram. Find x and y. (Lengths are in cm)
Name the quadrilaterals whose diagonals bisect each other
If the ratio of measures of two adjacent angles of a parallelogram is 1 : 2, find the measures of all angles of the parallelogram.
Construct ☐ BARC such that l(BA) = l(BC) = 4.2 cm, l(AC) = 6.0 cm, l(AR) = l(CR) = 5.6 cm
ABCD is a parallelogram. What kind of quadrilateral is it if: AC is perpendicular to BD but is not equal to it?
In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD. Prove that :
(i) AE = AD,
(ii) DE bisects and ∠ADC and
(iii) 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 c and f
ABCD is a parallelogram. Find the value of x, y and z.
