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.
संबंधित प्रश्न
Consider the given parallelograms. Find the values of the unknowns x, y, z.
Can a quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180°?
Find the measure of ∠P and ∠S, if `bar(SP) || bar(RQ)` in the following figure. (If you find m∠R, is there more than one method to find m∠P?).
Ratio of consecutive angles of a quadrilateral is 1 : 2 : 3 : 4. Find the measure of its each angle. Write, with reason, what type of a quadrilateral it is.
In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.
If a triangle and a parallelogram lie on the same base and between the same parallels, then prove that the area of the triangle is equal to half of the area of parallelogram
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 ______.
ABCD is a parallelogram. Points P and Q are taken on the sides AB and AD respectively and the parallelogram PRQA is formed. If ∠C = 45°, find ∠R.
Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.
The following figure RUNS is parallelogram. Find x and y. (Lengths are in cm)
