## Lakshya Education MCQs

Question:

If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a

a) Rhombus

b) Rectangle

c) Trapezium

d) Parallelogram
Options:

: In a rectangle, the diagonals are equal and bisect each other.

Hence, (b) is the correct option.

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## More Questions on This Topic :

Question 1.

A polygon is regular if all of its sides are equal.

: False
By definition of a regular polygon, we know that a polygon is regular if all sides and all angles are equal.
Question 2.

Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, O=120,R=105 and A=135? If not, why?

: No,
Given measures are
OA = 5 cm, O=120,R=105 and A=135
Here, we see that, O+R+A=120+105+135=360
i.e. the sum of three angles of a quadrilateal is 360.
This is impossible, as the total sum of four angles is 360 in a quadrilateral.
Hence, this quadrilateral cannot be constructed.
Question 3.

To construct a unique parallelogram, the minimum number of measurements required is

a) 2

b) 3

c) 4

d) 5

: We know that, in a parallelogram, opposite sides are equal and parallel. Also, opposite angles are equal.
So, to construct a parallelogram uniquely, we require the measure of any two non-parallel sides and the measure of an angle.
Hence, the minimum number of measurements required to construct a unique parallelogram is 3.
Question 4.

A quadrilateral can be drawn, if three sides and two diagonals are given.

: True
A quadrilateral can be drawn, if three sides and two diagonals are given.
Question 5.

In the given parallelogram YOUR, RUO=120 and OY is extended to point S, such that SRY=50. Find YSR.

: Given, RUO=120 and SRY=50
RYO=RUO=120 [ opposite angles of a parallelogram]
Now, SYR=180RYO [linear pair]
=180120=60
In ΔSRY,
By the angle sum property of a triangle, SRY+RYS+YSR=180
50+60+YSR=180YSR=180(50+60)=70.
Question 6.

The sum of all exterior angles of a polygon is .

: 360

The sum of all exterior angles of a polygon is always 360.