### Introduction to quadrilateral / Types of quadrilateral

**Tags:**Types of quadrilateral for grade 5,Free Worksheet PDF on Types of quadrilateral, Lesson on Introduction to quadrilateral for class 5, Quadrilateral properties practice page, Types of quadrilateral worksheet PDF, Square, Rectangle, Rhombus, and Trapezium, What is a parallelogram? Classification of Quadrilaterals, Properties of parallelograms, Parts or Elements of a Quadrilateral, A quadrilateral has three angles equal to 60°, 75° and 120°. Find its unknown angle. In a quadrilateral EFGH, ∠E = ∠F = 65° and ∠G = 120°, find ∠H. If the sum of 3 angles of a quadrilateral is 280°, find its fourth angle. Find the measure of the missing angles in a parallelogram, if ∠A = 55°, In a quadrilateral ABCD, ∠A = 105°, ∠B = 95°, ∠C= 70. Find ∠D. A quadrilateral is parallelogram whose opposite sides are parallel and equal in length. A rectangle is a parallelogram in which opposite sides are equal in length and each angles measure 90°. sum of the angles of a triangle = 180°Quadrilateral

Quadrilateral means "four sides" (quad means four, lateral means side).So, A closed figure made up of four line segments is called a

__quadrilateral__. It is 2-dimensional (a flat shape) closed (the lines join up) figure made up of 4 straight lines.The below figure is called a

__quadrilateral__. It can be named in the following ways: ABCD or BCDA or CDAB or DABC**Parts or Elements of a Quadrilateral**(i)

__Four__points A, B, C, D are called its__vertices.__(ii)

__Four__line segments AB, BC, CD and DA are called its__sides__.(iii) ∠DAB, ∠ABC, ∠BCD and ∠CDA are called its angles, and can also be written as ∠A, ∠B, ∠C and ∠D respectively. Angles are

__four__in total.(iv) The

__two__Line segments AC and BD are called its__diagonals__. (A line segment joining a pair of opposite vertices is called a diagonal.)(v) The interior angles add up to 360 degrees.

**TYPES OF QUADRILATERALS****Parallelogram**A quadrilateral is

__parallelogram__whose opposite sides are parallel and equal in length. Also its opposite angles are equal. Example: rectangle, square and rhombus.Here, ABCD is a parallelogram and

a) AB ∥ DC and AD ∥ BC.

b) AB = DC; AD = BC

c) ∠A = ∠C; ∠B = ∠D

**Rectangle**A

__rectangle__is a parallelogram in which opposite sides are equal in length and each angles measure 90°.Here, ABCD is a rectangle and

a) AB ∥ DC, AD ∥ BC

b) AD = BC; AB = DC

c) ∠A = ∠B = ∠C = ∠D = 90°

**Square**A

__square__is a parallelogram in which all sides are equal in length and each angle measure 90°. It is a rectangle in which all sides are equal.Here, ABCD is a square and

a) AB ∥ DC, AD ∥ BC

b) AB = BC = CD = DA

c) ∠A = ∠B = ∠ C = ∠D = 90°

**Rhombus**A

__rhombus__is a parallelogram whose all sides are equal. A rhombus is sometimes called a diamond.Here, ABCD is a rhombus and

a) AB ∥ DC, AD ∥ BC

b) AB = BC = CD = DA

c) ∠A = ∠C and ∠ B = ∠D (opposite angles are equal)

**Trapezium**A

__trapezium__is a quadrilateral which has a pair of opposite sides parallel.Here, ABCD is a trapezium and AB ∥ DC

**Note:**If a trapezium has non parallel sides equal, it is called__isosceles trapezium.__Here, ABCD is a isosceles trapezium and

a) AD ∥ BC

b) AB = BC

**Sum of Angles of a Quadrilateral**Let us join the opposite vertices of a quadrilateral ABCD.

Now we see two triangles in this figure.

We know that the sum of the angles of a triangle = 180°

As there are two triangles, therefore, the sum of angles of two triangles is 180° + 180° = 360°

So, sum of the angles of a quadrilateral = 360°

**Note:**No matter what the shape of quadrilateral is, the sum of four angles of a quadrilateral is 360°**Example 1:**In a quadrilateral ABCD, ∠A = 80°, ∠B = 105° and ∠C = 115°. Find ∠D.__Solution:__We know that the sum of four angles of a quadrilateral ABCD is 360°Or ∠A + ∠B + ∠C + ∠D = 360°

80° + 105° + 115° + ∠D = 360°

300° + ∠D = 360°

∠D = 360° – 300° = 60°

**Example 2:**Find the measure of the missing angles in a parallelogram, if ∠A = 60°.__Solution:__We know that the opposite angles of a parallelogram are equal, so, ∠C will also measure 60°.__Sum of angles of a quadrilateral = 360°__Or ∠A + ∠B + ∠C + ∠D = 360°

60° + ∠B + 60° + ∠D = 360° (As ∠A = ∠C)

∠B + ∠D + 120° = 360°

∠B + ∠D = 360° – 120° = 240°

But ∠B = ∠D (as opposite angles of a parallelogram are equal)

∠B = ∠D = 240°/2 = 120°

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