Types of Quadrilaterals

Types of quadrilaterals are discussed here:

In a quadrilateral family, each member has four sides, four vertices and four angles.

1. Rectangle:

A rectangle is a parallelogram in which all the angles are right angles.

Here ABCD is a rectangle.

(i) So, AB is parallel to DC.

AD is parallel to BC.

(ii) AD = BC

   AB = DC

(iii) ∠A = ∠B = ∠C = ∠D = 90°

Definition of Rectangle:

A parallelogram having each angle a right angle is called a rectangle.

In the figure, ABCD is a rectangle, in which AB || DC, AD || BC, AB = CD, AD = BC and diagonal AC = diagonal BD and all angles are right angles.

2. Square:

A square is a rectangle in which all sides are equal.

Here ABCD is a square.

(i) AB is parallel to DC.

BC is parallel to AD.

(ii) AB = BC = CD = DA.

(iii) ∠A = ∠B = ∠C = ∠D = 90°

Definition of Square:

A parallelogram having all sides equal and all angles of right angles is called a square.

In the figure, ABCD is a square, in which AB || DC, AD || BC, AB = BC = CD = DA and ∠A = ∠B = ∠C = ∠D =90°.

3. Trapezium:

A quadrilateral is called trapezium if a pair of its opposite sides are parallel.

Here ABCD is a trapezium.

AB is parallel to DC.

Definition of Trapezium:

A quadrilateral having one pair of parallel sides is called trapezium. Other pair of opposite sides may or may not be parallel.

In the above figure, ABCD is a trapezium, in which AB ||DC

Note:

If a trapezium has non parallel sides equal, it is called isosceles trapezium.

An isosceles trapezium is a quadrilateral having exactly one pair of parallel sides and the non-parallel sides are of equal length. i.e., AB || CD and AD = BC

4. Parallelogram:

A quadrilateral whose opposite sides are parallel and equal is called a parallelogram. Its opposite angles are equal.

Here LMNO is a parallelogram.

(i) LM is parallel to ON.

LO is parallel to MN.

(ii) LO = MN

     LM = ON

(iii) ∠L = ∠N

     ∠M = ∠O

Definition of Parallelogram:

A quadrilateral having both pairs of opposite sides parallel is called a parallelogram.

In the figure, ABCD is a parallelogram, in which AB || DC and AD || BC.

Note: All parallelogram are trapezium but all trapezium are not parallelogram.

5. Rhombus:

A rhombus is a parallelogram whose all sides are equal, opposite sides are parallel and opposite angles are equal.

Here LMNO is a rhombus.

(i) LM = MN = NO = OL

(ii) ∠L = ∠N

    ∠O = ∠M

(iii) LM is parallel to ON

OL is parallel to MN

Definition of Rhombus:

A parallelogram having all sides equal is called a rhombus.

In the figure, ABCD is a rhombus, in which AB || DC, AD || BC and AB = BC = DC = DA

Let’s discuss about the properties of types of quadrilateral in the table below;

Comparing the sides and angles of the different quadrilateral are discussed above.

Identifying Features of Quadrilaterals:

Name of Quadrilateral	Identifying Features	Figures
1. Rectangle	A parallelogram with all angles right angles.
2. Square	A rhombus with all angles right angles.
3. Rhombus	A parallelogram with all sides equal.
4. Parallelogram	A quadrilateral having 2 pairs of opposite sides parallel and equal.
5. Kite	A quadrilateral having 2 pairs of adjacent sides equal.
6. Trapezium	A quadrilateral having 1 pair of opposite sides parallel.
7. Isosceles Trapezium	A trapezium with a pair of non-parallel opposite sides equal.

Questions and Answers on Types of Quadrilaterals:

1. From the figures given below, state which of the following are quadrilaterals?

Solution:

(i) No, it is a triangle containing 3 sides.

(ii) Yes, it is a quadrilateral with 4 sides.

(iii) No, is a hexagon with 6 sides.

(iv) Yes, it is a quadrilateral with 4 sides.

2. From the adjoining figure, state whether the following statements are true or false: 

(i) AB = DC

(ii) AB||BC

(iii) ∠BAD = ∠BCD

(iv) ∠ABC=∠DAB

Solution:

(i) True, since AB and DC are opposite sides of parallelogram ABCD.

(ii) False, since AB and BC are adjacent sides of parallelogram ABCD.

(iii) True, since ∠BAD and ∠BCD are opposite angles of parallelogram ABCD.

(iv) False, since ∠ABC and ∠DAB are adjacent angles of parallelogram ABCD.

3. How many rectangles can be found in the following figure? Name them.

Solution:

9 rectangles; ABCD, AGHD, GBCH, AEFB, EDCF, AGIE, GBFI, IFCH, IHDE

● Quadrilaterals.

Elements of a Quadrilateral.

Types of Quadrilaterals.

Parallel Lines.

Perpendicular Lines.

Construction of Perpendicular Lines by using a Protractor.

Sum of Angles of a Quadrilateral.

Worksheet on Quadrilateral.

Practice Test on Quadrilaterals.

5th Grade Geometry Page

5th Grade Math Problems

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