A quadrilateral whose opposite sides and all the angles are equal is a

a) Rectangle

b) Parallelogram

c) Square

d) Rhombus

: We know that in a rectangle, opposite sides and all the angles are equal.

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Question 1.

If the sum of interior angles is double the sum of exterior angles taken in an order of a polygon, then it is a hexagon.

: True
The sum of exterior angles of a hexagon is 360. The sum of interior angles of a hexagon is 720, which is double the sum of exterior angles.
Question 2.

If a diagonal of a quadrilateral bisects both the angles, then it is a

a) Kite

b) Parallelogram

c) Rhombus

d) Rectangle

: If a diagonal of a quadrilateral bisects both the angles, then it is a rhombus.
Question 3.

In parallelogram ABCD, the angle bisector of A bisects BC. Will angle bisector of B also bisect AD? Give reason.

: Given, ABCD is a parallelogram, bisector of A, bisects BC at F, i.e. 1=2, CF = FB.
ABFE is a parallelogram by construction [FEBA]
1=6 [alternate angle]

But 1=2 [given]
AB = FB [opposite sides to equal angles are equal] ..... (i)
Now, in ΔABO and ΔBOF, AB = BF [from Eq. (i)]
BO = BO [common]
AO = FO [diagonals of rhombus bisect each other]
3=4 [by CPCT]
Now, BF=12BC [given]
BF=12AD [BC = AD]
AE=12AD [BF = AE]
E is the mid-point of AD.
Question 4.

Find the value of x in the trapezium ABCD given below

: Given, a trapezium ABCD in which A=(x20),D=(x+40)
Since, in a trapezium, the angles between the parallel lines are supplementary,
Question 5.

The measure of ___ angle of a concave quadrilateral is more than 180.

: One
A concave polygon is a polygon in which at least one interior angle is more than 180.
Question 6.

A photo frame is in the shape of a quadrilateral, with one diagonal longer than the other. Is it a rectangle? Why or why not?

: No, it cannot be a rectangle because the diagonals of a rectangle are equal.

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