Quadrilaterals and Problems

What is Quadrilaterals

A quadrilateral is a polygon with four edges (or sides) and four vertices or corners. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on.

Types of Quadrilaterals

There are six basic types of quadrilaterals

1. Rectangle
2. Square
3. Parallelogram
4. Rhombus
5. Trapezium
6. Kite

Rectangle:

A rectangle is a quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). It can also be defined as a parallelogram containing a right angle.

Square:

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length.

Parallelogram:

A parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Rhombus:

A Rhombus is a flat shape with 4 equal straight sides. A rhombus looks like a diamond. All sides have equal length. Opposite sides are parallel, and opposite angles are equal (it is a Parallelogram). The altitude is the distance at right angles to two sides.

Trapezium:

A 4-sided flat shape with straight sides and NO parallel sides. Quadrilaterals – Square, Rectangle, Rhombus, Trapezoid, Parallelogram.

Kite:

A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. In contrast, a parallelogram also has two pairs of equal-length sides, but they are opposite to each other rather than adjacent.

Question: 1

In the rectangle, a = 5.76 cm. Find the values of S and x.

A ) S = 2.4 cm, x = 5.76 cm

B) x = 2.4 cm, S = 4.8 cm

C) S = x = 5.76 cm

D)x = 2.4 cm, S = 5.76 cm

Answer : A

Question: 2

The perimeters of two similar triangles are 2 in and 6 in. What is the corresponding side of the second triangle, if one side of the first triangle is 2 in?

A ) 12 in

B) 7 in

C) 16 in

D) 6 in

Answer : D

Question: 3

What is the angle between the diagonals of a rhombus?

A ) 60^o

B) 90^o

C) 45^o

D) 30^o

Answer : B

Question: 4

Which of the following are congruent in a rhombus?

A ) sides

B) diagonals

C) sides and diagonals

D) interior angles

Answer : A

Question: 5

What is the angle between the diagonals of a square?

A ) 45^o

B) 30^o

C) 90^o

D) 60^o

Answer : C