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प्रश्न
State, 'true' or 'false'
The diagonals of a rectangle bisect each other.
विकल्प
True
False
उत्तर
True.
This is true because we know that a rectangle is a parallelogram. So, all the properties of a parallelogram are true for a rectangle. Since the diagonals of a parallelogram bisect each other, the same holds true for a rectangle.
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संबंधित प्रश्न
Diagonal AC of a parallelogram ABCD bisects ∠A (see the given figure). Show that
- It bisects ∠C also,
- ABCD is a rhombus
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see the given figure). Show that:
- ΔAPD ≅ ΔCQB
- AP = CQ
- ΔAQB ≅ ΔCPD
- AQ = CP
- APCQ is a parallelogram
State, 'true' or 'false'
The diagonals of a quadrilateral bisect each other.
State, 'true' or 'false'
If the diagonals of a quadrilateral bisect each other at right angle, the quadrilateral is a square.
The given figure shows a square ABCD and an equilateral triangle ABP. 
Calculate: (i) ∠AOB
(ii) ∠BPC
(iii) ∠PCD
(iv) Reflex ∠APC
In the figure, if the area of ||gm PQRS is 84cm2; find the area of
(i) || gm PQMN
(ii) ΔPQS
(iii) ΔPQN
In the figure, PQR is a straight line. SQ is parallel to Tp. Prove that the quadrilateral PQST is equal in area to the ΔPSR.
In the given figure, if AB ∥ DC ∥ FG and AE is a straight line. Also, AD ∥ FC. Prove that: area of ∥ gm ABCD = area of ∥ gm BFGE.
In the given figure, PT ∥ QR and QT ∥ RS. Show that: area of ΔPQR = area of ΔTQS.
*Question modified
The diagonals of a parallelogram ABCD intersect at O. A line through O meets AB in P and CD in Q. Show that
(a) Area of APQD = `(1)/(2)` area of || gm ABCD
(b) Area of APQD = Area of BPQC
A quadrilateral ABCD is such that diagonals BD divides its area into two equal parts. Prove that BD bisects AC.
Find the area of a parallelogram whose base is 12cm and the height is 5cm.
One side of a parallelogram is 12cm and the altitude corresponding to i is 8cm. If the length of the altitude corresponding to its adjacent side is 16cm, find the length of the adjacent side.
A rectangular hall of 40m by 24m is covered with carpets of size 6m x 4m. Find the number of carpets required to cover the hall.
The area of a square garden is equal to the area of a rectangular plot of length 160m and width 40m. Calculate the cost of fencing the square garden at Rs.12per m.
Find the perimeter and area of a square whose diagonal is `5sqrt(2)"cm"`. Give your answer correct to two decimal places if `sqrt(2)` = 1.414.
The length and breadth of a rectangular field are in the ratio 8 : 5. A 2m wide path runs all around outside the field. The area of the path is 848m2. Find the length and breadth of the field.
All the sides of a rhombus are of equal length.
Examine whether the following is a polygon. If it is not, say why?
