In which of the following ways can four people hold each other's hands to form a quadrilateral?

A.

All four stand in one line

B.

Three stand in one line and one of them out of the line

C.

Two pairs of people stand facing each other

D.

Two pairs of people stand with their back facing and hold hands from behind and side.

#### SOLUTION

Solution : C and D

A figure formed by joining four points in an order is called a quadrilateral.
Consider the analogy of four people as four points.
In the first case, there are four collinear points which cannot form a quadrilateral.
In the second case, there are three collinear points which can form a triangle, but not a quadrilateral.
In the third case, the two pair of people face each other and thus form a quadrilateral.
In the fourth case, the two pair of people face exactly opposite but hold each others hands from behind and side and thus can for a quadrilateral.

A parallelogram whose all sides are equal is called a _____.

A.

trapezium

B.

rhombus

C.

rectangle

D.

kite

#### SOLUTION

Solution : B

• Trapezium cannot be a parallelogram.

• Rhombus is a parallelogram, whose sides are always equal.
• Rectangle is a parallelogram whose opposite sides are equal.
• Kite is not a parallelogram. A parallelogram whose all sides are equal is called a rhombus.

The angles of a quadrilateral are in the ratio 3:4:5:6. Find the angles of the quadrilateral.

A.

40, 100, 80, 140

B.

6080100120

C.

30405060

D.

10, 20, 30, 40

#### SOLUTION

Solution : B

The angles of a quadrilateral are in the ratio 3:4:5:6.

Let the angles of the quadrilateral be 3x,4x,5x,6x.

The sum of the angles of a quadrilateral is 360.
3x+4x+5x+6x=360
18x=360
x=20

3x=60,4x=80,5x=100,6x=120

The three angles of a quadrilateral are 40,80,90. The fourth angle is:

A.

150

B.

140

C.

180

D.

90

#### SOLUTION

Solution : A

According to the angle sum property of a quadrilateral, the sum of all the angles of a quadrilateral is =360

The fourth angle

=360-(40+80+90)
=360210
=150

Which of the following is a regular quadrilateral?

A.

Parallelogram

B.

Square

C.

Trapezium

D.

Kite

#### SOLUTION

Solution : B

A regular quadrilateral is a shape that has four equal sides with all the interior angles equal.
Among the given options, only square has all its four sides  equal with each angle being 90.

To determine all angles of a parallelogram, which of the following is the minimum necessary condition?

A.

Only one angle is known.

B.

Two angles are known.

C.

Three angles are known.

D.

Length of sides should be known

#### SOLUTION

Solution : A

If one angle of a parallelogram is known, the other angles can be found out by applying the following two properties:
1. The adjacent angles are supplementary.
2. The opposite angles are equal.

Area of parallelogram is the product of base and corresponding height.

A.

True

B. False

#### SOLUTION

Solution : A

A parallelogram is made up of two triangles, each having an area equal to the half of the product of base and corresponding height. Adding these two, we find the given statement to be true.

If one of the angles of a parallelogram is 80°, the other non-adjacent angle is ___degrees.

#### SOLUTION

Solution :

In a parallelogram, the opposite angles are equal. Hence, the non-adjacent angle is 80.

Quadrilateral in which only one pair of opposite sides is parallel is known as__

#### SOLUTION

Solution :

Trapezium is a quadrilateral in which only one pair of opposite sides is parallel.

A diagonal of a parallelogram divides it into two congruent triangles.

A.

True

B.

False

#### SOLUTION

Solution : A Suppose ABCD is a parallelogram and BD is the diagonal.
There are two triangles - Δ ABD and Δ CDB
In Δ ABD and Δ CDB,
AD = BC   (opposite sides of a parallelogram are equal)
AB = CD   (opposite sides of a parallelogram are equal)
BD is common
By SSS criterion of congruency,
Δ ABD Δ CDB
Hence, the given statement is true.