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प्रश्न
State, 'true' or 'false'
The diagonals of a parallelogram bisect each other at right angle.
विकल्प
True
False
उत्तर
False
Consider a rectangle as shown below.
It is a parallelogram. However, the diagonals of a rectangle do not intersect at right angles, even though they bisect each other.
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संबंधित प्रश्न
If the diagonals of a parallelogram are equal, then show that it is a rectangle.
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 quadrilateral, whose four sides are equal, is a square.
In the given figure ABCD is a rhombus with angle A = 67°
If DEC is an equilateral triangle, calculate:
- ∠CBE
- ∠DBE
In the given figure, PQRS is a ∥ gm. A straight line through P cuts SR at point T and QR produced at N. Prove that area of triangle QTR is equal to the area of triangle STN.
In the given figure, ST ∥ PR. Prove that: area of quadrilateral PQRS = area of ΔPQT.
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, ABC is a triangle and AD is the median.
If E is any point on the median AD. Show that: Area of ΔABE = Area of ΔACE.
In the given figure, ABC is a triangle and AD is the median.
If E is the midpoint of the median AD, prove that: Area of ΔABC = 4 × Area of ΔABE
Two adjacent sides of a parallelogram are 34 cm and 20 cm. If one of its diagonal is 42 cm, find: area of the parallelogram.
Find the perimeter of a rhombus whose diagonals are 24cm and 10cm.
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.
Find the area of a rhombus, whose one side and one diagonal measure 20cm and 24cm respectively.
A lawn in the shape of a rectangle is to be developed in front of a Marriage Hall. The length and breadth of the lawn are 44m and 32m. A space of 2m is left on the two shoulder sides and one longer side for flower and in the remaining area grass is laid. Calculate the area of the flower space and the area on which grass is laid.
Inside a square field of side 44m, a square flower bed is prepared leaving a graved path all round the flower bed. The total cost of laying the flower bed at Rs.25per sq m. and gravelling the path at Rs.120per sq m. is Rs.80320. Find the width of the gravel path.
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.
Each angle of a rectangle is a right angle.
The opposite sides of a trapezium are parallel.
Name polygon.
Make two more examples of this.
