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
The diagonal BD of a parallelogram ABCD bisects angles B and D. Prove that ABCD is a rhombus.
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: RT bisects angle R
ABCD is a parallelogram. The bisector of ∠BAD meets DC at P, and AD is half of AB.
Prove that: ∠APB is a right angle.
In the given figure, the perimeter of parallelogram PQRS is 42 cm. Find the lengths of PQ and PS.
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")`?
In parallelogram ABCD of the accompanying diagram, line DP is drawn bisecting BC at N and meeting AB (extended) at P. From vertex C, line CQ is drawn bisecting side AD at M and meeting AB (extended) at Q. Lines DP and CQ meet at O. Show that the area of triangle QPO is `9/8` of the area of the parallelogram ABCD
Which of the following statement is correct?
In the following figure, ABCD and AEFG are two parallelograms. If ∠C = 55º, determine ∠F.
Construct a parallelogram POUR in which, PO = 5.5 cm, OU = 7.2 cm and ∠O = 70°.
