Advertisements
Advertisements
प्रश्न
In parallelogram ABCD, X and Y are midpoints of opposite sides AB and DC respectively. Prove that:
(i) AX = YC
(ii) AX is parallel to YC
(iii) AXCY is a parallelogram.
Advertisements
उत्तर
Given: In parallelogram ABCD, X and Y are the mid-points of sides AB and DC respectively AY and CX are joined.
To prove :
(i) AX = YC
(ii) AX is parallel to YC
(iii) AXCY is a parallelogram
Proof: AB || DC and X and Y are the mid-points of the sides AB and DC respectively
(i) AX = YC ( 
(ii) and AX || YC
(iii) AXCY is a parallelogram (A pair of opposite sides are equal and parallel)
Hence proved.
APPEARS IN
संबंधित प्रश्न
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°?
In parallelogram ABCD, ∠A = 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram, if AB = 5x – 7 and CD = 3x +1 ; find the length of CD.
Given: Parallelogram ABCD in which diagonals AC and BD intersect at M.
Prove: M is the mid-point of LN.
Prove that the diagonals of a parallelogram bisect each other.
In the given figure, AB || EC, AB = AC and AE bisects ∠DAC. Prove that:
- ∠EAC = ∠ACB
- ABCE is a parallelogram.
Which of the following figures satisfy the following properties?
- All sides are congruent.
- All angles are right angles.
- Opposite sides are parallel.
If opposite angles of a quadrilateral are equal, it must be a parallelogram.
ABCD is a parallelogram. Find the value of x, y and z.
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
