A polygon comes under which of the following categories?

A.

Plane figure

B.

Simple Closed Curve

C.

Curve not closed

D.

3D representation

#### SOLUTION

Solution : A and B

The polygon is a simple closed curve made up of line segments. Each line segment represents a side of a polygon.

The polygon is also a plane figure with atleast three sides and three angles.

The sum of exterior angles of a polygon (in degrees) with 10 sides is

___.

#### SOLUTION

Solution : The sum of all exterior angles of a polygon, irrespective of the number of its sides, is equal to 360. If the polygon is regular, the measure of each exterior angle can be calculated by dividing 360 by the total number of sides in the polygon.

A quadrilateral has two of its angles as 30 and 40. What type of quadrilateral can it be?

A.

Trapezium

B. Square
C.

Parallelogram

D.

Rectangle

#### SOLUTION

Solution : A

In square and rectangle each angle is 900.

In a parallelogram, two adjacent angles have to be either equal or supplementary. The angles 30 and 40 are neither supplementary nor equal. So, the two angles cannot belong to a parallelogram.

For trapezium, there are no such restrictions. So, the given qudrilateral is a trapezium.

A square is also a

A.

Rhombus

B.

Parallelogram

C. Rectangle
D.

Trapezium

#### SOLUTION

Solution : A, B, and C

A square is a parallelogram because it has opposite pairs of sides parallel and equal.

It is also a rhombus because it has all its sides equal, opposite sides are parallel and the diagonals intersect at 90.

A square is also a rectangle because all its angles are 90 and its pair of opposite sides are equal and parallel.

A square can't be a trapezium as in trapezium only one of the opposite sides are parallel.

Consider the figure shown. What type of quadrilateral can it be?

A. Rhombus
B.

Parallelogram

C.

Kite

D.

Triangle

#### SOLUTION

Solution : B

In the given figure the pair of opposite sides are parallel and equal. So, the given figure is a parallelogram.

Among the options, the quadrilateral ABCD can be either 'Rhombus' or 'Parallelogram'.  [ Rhombus is also a parallelogram]

But adajcent sides of ABCD are not equal (ie, AD and CD are not equal).

So, ABCD cannot be a rhombus. Hence, ABCD is a paralleogram.

The number of sides in a kite is

___.

#### SOLUTION

Solution :

A kite is a quadrilateral. Hence it has 4 sides.

I draw a quadrilateral and then draw all its diagonals.How many triangles can I find?

A.

3

B.

2

C.

8

D.

1

#### SOLUTION

Solution : C

The triangles are-
ΔABD,ΔCBD,ΔABC,ΔDCA,ΔAED,ΔCED,ΔBEC,ΔAEB

There are 8 triangles in the figure.

In parallelogram ABCD, which of the two angles are equal?

A.

Angles A & B

B.

Angles B & C

C.

Angles A & C

D.

Angles C & D

#### SOLUTION

Solution : C

In a parallelogram, the two opposite angles are equal. Hence, if the four vertices of a parallelogram are A, B, C, D in cyclic order, then A & C and    B & D are equal.

In parallelogram ABCD, which of the 2 sides are equal?

A.

AB & BC

B.

C.

CD & BC

D.

AB & CD

#### SOLUTION

Solution : D

The opposite sides of a parallelogram are equal.
Hence, sides AB & CD (if the cyclic order of the vertices are A, B, C, D) are opposite sides and are equal.

There is a pair of parallel lines which intersects with another pair of parallel lines. The quadrilateral formed is trapezium.

A.

True

B.

False

#### SOLUTION

Solution : B

The quadrilateral formed between two pairs of parallel lines is a parallelogram. In a trapezium, the only one pair of opposite sides is parallel.