Advertisements
Advertisements
प्रश्न
In the given figure, ABCD is a parallelogram.
Prove that: AB = 2 BC.
Advertisements
उत्तर
Given ABCD is a parallelogram
To prove: AB = 2BC
Proof: ABCD is a parallelogram
A + D + B + C = 180°
From the AEB we have
⇒ `("∠A")/(2) + ("∠B")/(2)` + E = 180°
⇒ ∠A - `("∠A")/(2)` + ∠D + ∠E1 = 180° ...[taking E1 as new angle]
⇒ ∠A + ∠D + ∠E1 = 180° + `("∠A")/(2)`
⇒ ∠E1 = `("∠A")/(2)` ...[Since ∠A + ∠D = 180°]
Again,
similarly,
∠E1 = `("∠B")/(2)`
Now
AB = DE + EC
= AD + BC
= BC + BC
= 2BC ...[since AD = BC]
Hence, proved.
APPEARS IN
संबंधित प्रश्न
E is the mid-point of side AB and F is the mid-point of side DC of parallelogram ABCD. Prove that AEFD is a parallelogram.
The alongside figure shows a parallelogram ABCD in which AE = EF = FC.
Prove that:
- DE is parallel to FB
- DE = FB
- DEBF is a parallelogram.
In parallelogram ABCD, the bisector of angle A meets DC at P and AB = 2 AD.
Prove that:
(i) BP bisects angle B.
(ii) Angle APB = 90o.
Points M and N are taken on the diagonal AC of a parallelogram ABCD such that AM = CN. Prove that BMDN is a parallelogram.
PQRS is a parallelogram. T is the mid-point of PQ and ST bisects ∠PSR.
Prove that: ∠RTS = 90°
In a parallelogram ABCD, E is the midpoint of AB and DE bisects angle D. Prove that:CE is the bisector of angle C and angle DEC is a right angle
In the given figure, the perimeter of parallelogram PQRS is 42 cm. Find the lengths of PQ and PS.
Find the perimeter of the parallelogram PQRS.
In the Figure, ABCD is a rectangle and EFGH is a parallelogram. Using the measurements given in the figure, what is the length d of the segment that is perpendicular to `bar("HE")` and `bar("FG")`?
Which of the following statement is correct?
