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प्रश्न
State, 'true' or 'false'
If the diagonals of a quadrilateral bisect each other at right angle, the quadrilateral is a square.
विकल्प
True
False
उत्तर
False
Observe the above figure. The diagonals of the quadrilateral shown above bisect each other at right angles, however, the quadrilateral need not be a square, since the angles of the quadrilateral are clearly not right angles.
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संबंधित प्रश्न
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
ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). Show that
- ∠A = ∠B
- ∠C = ∠D
- ΔABC ≅ ΔBAD
- diagonal AC = diagonal BD
[Hint: Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]
State, 'true' or 'false'
The diagonals of a parallelogram bisect each other at right angle.
State, 'true' or 'false'
Diagonals of a rhombus are equal.
In the following figures, ABCD is a parallelogram.
find the values of x and y.
In a square ABCD, diagonals meet at O. P is a point on BC such that OB = BP.
Show that:
- ∠POC = `[ 22 ( 1°)/( 2 ) ]`
- ∠BDC = 2 ∠POC
- ∠BOP = 3 ∠CPO
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
Prove that the median of a triangle divides it into two triangles of equal area.
The length of a rectangular field is thrice of its width. If the perimeter of this field is 1.6km, find its area in sq.m.
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 perimeter of a square plot of land is 64m. The area of a nearby rectangular plot is 24m2 more than the area of the given square. If the length of the rectangle is 14m, find its breadth.
A rectangular field is 240m long and 180m broad. In one corner a farm house is built on a square plot of side 40m. Find the area of the remaining portion and the cost of fencing the open sides Rs.25per m.
A footpath of uniform width runs all around the inside of a rectangular garden of 40 m x 30 m. If the path occupies 136 m2, find the width of the path.
ABCD is a trapezium in which AB || DC and ∠A = ∠B = 45º. Find angles C and D of the trapezium.
Give reasons for the following :
A rectangle can be thought of as a special parallelogram.
Give reason for the following :
Square is also a parallelogram.
Examine whether the following is a polygon. If it is not, say why?
Examine whether the following is a polygon. If it is not, say why?
Name polygon.
Make two more examples of this.
