Advertisements
Advertisements
प्रश्न
In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.
Advertisements
उत्तर
Given: Parallelogram ABCD in which E and F are mid-points of AD and BC respectively.
To Prove: BFDE is a Parallelogram.
Proof: E is the mid-point of AD. (Given)
DE = `1/2`
Also, F is mid-point of BC (Given)
BF = `1/2`
But AD = BC (opp. sides of parallelogram)
BF = DE
Again AD || BC
⇒ DE || BF
Now DE || BF and DE = BF
Hence BFDE is a parallelogram.
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 = ______
Name the quadrilaterals whose diagonals bisect each other
Perimeter of a parallelogram is 150 cm. One of its sides is greater than the other side by 25 cm. Find the lengths of all sides.
In the given figure, `square`PQRS and `square`ABCR are two parallelograms. If ∠P = 110° then find the measures of all angles of `square`ABCR.
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.
Construct a parallelogram ABCD such that l(BC) = 7 cm, m∠ABC = 40° , l(AB) = 3 cm.
Find the values of x and y in the following parallelogram.
The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is 45°. Find the angles of the parallelogram.
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.
The following figure RUNS is parallelogram. Find x and y. (Lengths are in cm)
