# NCERT Solutions for Class 8 Maths Chapter 3- Understanding Quadrilaterals

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals, are provided here, which can be downloaded for free in PDF format. The NCERT Solutions for chapter Understanding Quadrilaterals are prepared by the mathematics experts at BYJUโS, keeping the examination point of view in mind. These solutions explains the accurate method of solving problems. By understanding the concepts used in NCERT Solutions for Class 8, students will be able to clear all their doubts related to Understanding Quadrilaterals.

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## Exercise 3.1 Page: 41

**1. Given here are some figures.**

**Classify each of them on the basis of the following.**

**Simple curve (b) Simple closed curve (c) Polygon**

**(d) Convex polygon (e) Concave polygon**

Solution:

a) Simple curve: 1, 2, 5, 6 and 7

b) Simple closed curve: 1, 2, 5, 6 and 7

c) Polygon: 1 and 2

d) Convex polygon: 2

e) Concave polygon: 1

**2. How many diagonals does each of the following have?**

**a) A convex quadrilateral (b) A regular hexagon (c) A triangle**

Solution:

a) A convex quadrilateral: 2.

b) A regular hexagon: 9.

c) A triangle: 0

**3. What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)**

Solution:

Let ABCD be a convex quadrilateral.

From the figure, we infer that the quadrilateral ABCD is formed by two triangles,

i.e. ฮADC and ฮABC.

Since, we know that sum of interior angles of triangle is 180ยฐ,

the sum of the measures of the angles is 180ยฐ + 180ยฐ = 360ยฐ

Let us take another quadrilateral ABCD which is not convex .

Join BC, Such that it divides ABCD into two triangles ฮABC and ฮBCD. In ฮABC,

โ 1 + โ 2 + โ 3 = 180ยฐ (angle sum property of triangle)

In ฮBCD,

โ 4 + โ 5 + โ 6 = 180ยฐ (angle sum property of triangle)

โด, โ 1 + โ 2 + โ 3 + โ 4 + โ 5 + โ 6 = 180ยฐ + 180ยฐ

โ โ 1 + โ 2 + โ 3 + โ 4 + โ 5 + โ 6 = 360ยฐ

โ โ A + โ B + โ C + โ D = 360ยฐ

Thus, this property hold if the quadrilateral is not convex.

**4. Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)**

**What can you say about the angle sum of a convex polygon with number of sides? (a) 7 (b) 8 (c) 10 (d) n**

Solution:

The angle sum of a polygon having side n = (n-2)ร180ยฐ

a) 7

Here, n = 7

Thus, angle sum = (7-2)ร180ยฐ = 5ร180ยฐ = 900ยฐ

b) 8

Here, n = 8

Thus, angle sum = (8-2)ร180ยฐ = 6ร180ยฐ = 1080ยฐ

c) 10

Here, n = 10

Thus, angle sum = (10-2)ร180ยฐ = 8ร180ยฐ = 1440ยฐ

d) n

Here, n = n

Thus, angle sum = (n-2)ร180ยฐ

**5. What is a regular polygon?**

**State the name of a regular polygon of**

**(i) 3 sides (ii) 4 sides (iii) 6 sides **Solution:

Regular polygon: A polygon having sides of equal length and angles of equal measures is called regular polygon. i.e., A regular polygon is both equilateral and equiangular.

(i) A regular polygon of 3 sides is called equilateral triangle.

(ii) A regular polygon of 4 sides is called square.

(iii) A regular polygon of 6 sides is called regular hexagon.

**6. Find the angle measure x in the following figures.**

Solution:

a) The figure is having 4 sides. Hence, it is a quadrilateral. Sum of angles of the quadrilateral = 360ยฐ

โ 50ยฐ + 130ยฐ + 120ยฐ + x = 360ยฐ

โ 300ยฐ + x = 360ยฐ

โ x = 360ยฐ โ 300ยฐ = 60ยฐ

b) The figure is having 4 sides. Hence, it is a quadrilateral. Also, one side is perpendicular forming right angle.

Sum of angles of the quadrilateral = 360ยฐ

โ 90ยฐ + 70ยฐ + 60ยฐ + x = 360ยฐ

โ 220ยฐ + x = 360ยฐ

โ x = 360ยฐ โ 220ยฐ = 140ยฐ

c) The figure is having 5 sides. Hence, it is a pentagon.

Sum of angles of the pentagon = 540ยฐ Two angles at the bottom are linear pair.

โด, 180ยฐ โ 70ยฐ = 110ยฐ

180ยฐ โ 60ยฐ = 120ยฐ

โ 30ยฐ + 110ยฐ + 120ยฐ + x + x = 540ยฐ

โ 260ยฐ + 2x = 540ยฐ

โ 2x = 540ยฐ โ 260ยฐ = 280ยฐ

โ 2x = 280ยฐ

= 140ยฐ

d) The figure is having 5 equal sides. Hence, it is a regular pentagon. Thus, its all angles are equal.

5x = 540ยฐ

โ x = 540ยฐ/5

โ x = 108ยฐ

**7.**

Solution:

a) Sum of all angles of triangle = 180ยฐ

One side of triangle = 180ยฐ- (90ยฐ + 30ยฐ) = 60ยฐ

x + 90ยฐ = 180ยฐ โ x = 180ยฐ โ 90ยฐ = 90ยฐ

y + 60ยฐ = 180ยฐ โ y = 180ยฐ โ 60ยฐ = 120ยฐ

z + 30ยฐ = 180ยฐ โ z = 180ยฐ โ 30ยฐ = 150ยฐ

x + y + z = 90ยฐ + 120ยฐ + 150ยฐ = 360ยฐ

b) Sum of all angles of quadrilateral = 360ยฐ

One side of quadrilateral = 360ยฐ- (60ยฐ + 80ยฐ + 120ยฐ) = 360ยฐ โ 260ยฐ = 100ยฐ

x + 120ยฐ = 180ยฐ โ x = 180ยฐ โ 120ยฐ = 60ยฐ

y + 80ยฐ = 180ยฐ โ y = 180ยฐ โ 80ยฐ = 100ยฐ

z + 60ยฐ = 180ยฐ โ z = 180ยฐ โ 60ยฐ = 120ยฐ

w + 100ยฐ = 180ยฐ โ w = 180ยฐ โ 100ยฐ = 80ยฐ

x + y + z + w = 60ยฐ + 100ยฐ + 120ยฐ + 80ยฐ = 360ยฐ

## Exercise 3.2 Page: 44

**1. Find x in the following figures.**

Solution:

a)

125ยฐ + m = 180ยฐ โ m = 180ยฐ โ 125ยฐ = 55ยฐ (Linear pair)

125ยฐ + n = 180ยฐ โ n = 180ยฐ โ 125ยฐ = 55ยฐ (Linear pair)

x = m + n (exterior angle of a triangle is equal to the sum of 2 opposite interior 2 angles)

โ x = 55ยฐ + 55ยฐ = 110ยฐ

b)

Two interior angles are right angles = 90ยฐ

70ยฐ + m = 180ยฐ โ m = 180ยฐ โ 70ยฐ = 110ยฐ (Linear pair)

60ยฐ + n = 180ยฐ โ n = 180ยฐ โ 60ยฐ = 120ยฐ (Linear pair) The figure is having five sides and is a pentagon.

Thus, sum of the angles of pentagon = 540ยฐ 90ยฐ + 90ยฐ + 110ยฐ + 120ยฐ + y = 540ยฐ

โ 410ยฐ + y = 540ยฐ โ y = 540ยฐ โ 410ยฐ = 130ยฐ

x + y = 180ยฐ (Linear pair)

โ x + 130ยฐ = 180ยฐ

โ x = 180ยฐ โ 130ยฐ = 50ยฐ

**2. Find the measure of each exterior angle of a regular polygon of**

**(i) 9 sides (ii) 15 sides **Solution:

Sum of angles a regular polygon having side n = (n-2)ร180ยฐ

(i) Sum of angles a regular polygon having side 9 = (9-2)ร180ยฐ= 7ร180ยฐ = 1260ยฐ

Each interior angle=1260/9 = 140ยฐ

Each exterior angle = 180ยฐ โ 140ยฐ = 40ยฐ

Or,

Each exterior angle = sum of exterior angles/Number of angles = 360/9 = 40ยฐ

(ii) Sum of angles a regular polygon having side 15 = (15-2)ร180ยฐ

= 13ร180ยฐ = 2340ยฐ

Each interior angle = 2340/15 = 156ยฐ

Each exterior angle = 180ยฐ โ 156ยฐ = 24ยฐ

Or,

Each exterior angle = sum of exterior angles/Number of angles = 360/15 = 24ยฐ

**3. How many sides does a regular polygon have if the measure of an exterior angle is 24ยฐ? Solution:**

Each exterior angle = sum of exterior angles/Number of angles

24ยฐ= 360/ Number of sides

โ Number of sides = 360/24 = 15

Thus, the regular polygon has 15 sides.

## 4. How many sides does a regular polygon have if each of its interior angles is 165ยฐ? Solution:

Interior angle = 165ยฐ

Exterior angle = 180ยฐ โ 165ยฐ = 15ยฐ

Number of sides = sum of exterior angles/ exterior angles

โ Number of sides = 360/15 = 24

Thus, the regular polygon has 24 sides.

**5.**

**a) Is it possible to have a regular polygon with measure of each exterior angle as 22ยฐ?**

**b) Can it be an interior angle of a regular polygon? Why?**

Solution:

a) Exterior angle = 22ยฐ

Number of sides = sum of exterior angles/ exterior angle

โ Number of sides = 360/22 = 16.36

No, we canโt have a regular polygon with each exterior angle as 22ยฐ as it is not divisor of 360.

b) Interior angle = 22ยฐ

Exterior angle = 180ยฐ โ 22ยฐ= 158ยฐ

No, we canโt have a regular polygon with each exterior angle as 158ยฐ as it is not divisor of 360.

## 6.

**a) What is the minimum interior angle possible for a regular polygon? Why?**

**b) What is the maximum exterior angle possible for a regular polygon?**

Solution:

a) Equilateral triangle is regular polygon with 3 sides has the least possible minimum interior angle because the regular with minimum sides can be constructed with 3 sides at least.. Since, sum of interior angles of a triangle = 180ยฐ

Each interior angle = 180/3 = 60ยฐ

b) Equilateral triangle is regular polygon with 3 sides has the maximum exterior angle because the regular polygon with least number of sides have the maximum exterior angle possible. Maximum exterior possible = 180 โ 60ยฐ = 120ยฐ

## Exercise 3.3 Page: 50

**1. Given a parallelogram ABCD. Complete each statement along with the definition or property used.**

(i) AD = โฆโฆ (ii) โ DCB = โฆโฆ

(iii) OC = โฆโฆ (iv) m โ DAB + m โ CDA = โฆโฆ

Solution:

(i) AD = BC (Opposite sides of a parallelogram are equal)

(ii) โ DCB = โ DAB (Opposite angles of a parallelogram are equal) (iii) OC = OA (Diagonals of a parallelogram are equal)

(iv) m โ DAB + m โ CDA = 180ยฐ

**2. Consider the following parallelograms. Find the values of the unknown x, y, z**

Solution:

(i)

y = 100ยฐ (opposite angles of a parallelogram)

x + 100ยฐ = 180ยฐ (Adjacent angles of a parallelogram)

โ x = 180ยฐ โ 100ยฐ = 80ยฐ

x = z = 80ยฐ (opposite angles of a parallelogram)

โด, x = 80ยฐ, y = 100ยฐ and z = 80ยฐ

(ii)

50ยฐ + x = 180ยฐ โ x = 180ยฐ โ 50ยฐ = 130ยฐ (Adjacent angles of a parallelogram) x = y = 130ยฐ (opposite angles of a parallelogram)

x = z = 130ยฐ (corresponding angle)

(iii)

x = 90ยฐ (vertical opposite angles)

x + y + 30ยฐ = 180ยฐ (angle sum property of a triangle)

โ 90ยฐ + y + 30ยฐ = 180ยฐ

โ y = 180ยฐ โ 120ยฐ = 60ยฐ

also, y = z = 60ยฐ (alternate angles)

(iv)

z = 80ยฐ (corresponding angle) z = y = 80ยฐ (alternate angles) x + y = 180ยฐ (adjacent angles)

โ x + 80ยฐ = 180ยฐ โ x = 180ยฐ โ 80ยฐ = 100ยฐ

(v)

x=28o

y = 112o z = 28o

**3. Can a quadrilateral ABCD be a parallelogram if (i) โ D + โ B = 180ยฐ?**

**(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?**

**(iii)โ A = 70ยฐ and โ C = 65ยฐ?**

Solution:

(i) Yes, a quadrilateral ABCD be a parallelogram if โ D + โ B = 180ยฐ but it should also

fulfilled some conditions which are:

(a) The sum of the adjacent angles should be 180ยฐ.

(b) Opposite angles must be equal.

(ii) No, opposite sides should be of same length. Here, AD โ BC

(iii) No, opposite angles should be of same measures. โ A โ โ C

**4. Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.**

Solution:

ABCD is a figure of quadrilateral that is not a parallelogram but has exactly two opposite

angles that is โ B = โ D of equal measure. It is not a parallelogram because โ A โ โ C.

**5. The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.**

Solution:

Let the measures of two adjacent angles โ A and โ B be 3x and 2x respectively in

parallelogram ABCD.

โ A + โ B = 180ยฐ

โ 3x + 2x = 180ยฐ

โ 5x = 180ยฐ

โ x = 36ยฐ

We know that opposite sides of a parallelogram are equal.

โ A = โ C = 3x = 3 ร 36ยฐ = 108ยฐ

โ B = โ D = 2x = 2 ร 36ยฐ = 72ยฐ

**6. Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.**

Solution:

Let ABCD be a parallelogram.

Sum of adjacent angles of a parallelogram = 180ยฐ

โ A + โ B = 180ยฐ

โ 2โ A = 180ยฐ

โ โ A = 90ยฐ

also, 90ยฐ + โ B = 180ยฐ

โ โ B = 180ยฐ โ 90ยฐ = 90ยฐ

โ A = โ C = 90ยฐ

โ B = โ D = 90

ยฐ

**7. The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.**

Solution:

y = 40ยฐ (alternate interior angle)

โ P = 70ยฐ (alternate interior angle)

โ P = โ H = 70ยฐ (opposite angles of a parallelogram)

z = โ H โ 40ยฐ= 70ยฐ โ 40ยฐ = 30ยฐ

โ H + x = 180ยฐ

โ 70ยฐ + x = 180ยฐ

โ x = 180ยฐ โ 70ยฐ = 110ยฐ

**8. The following figures GUNS and RUNS are parallelograms. Find x and y. (Lengths are in cm)**

Solution:

(i) SG = NU and SN = GU (opposite sides of a parallelogram are equal) 3x = 18

x = 18/3

โ x =6

3y โ 1 = 26 an

d,

โ 3y = 26 + 1

โ y = 27/3=9

x = 6 and y = 9

(ii) 20 = y + 7 and 16 = x + y (diagonals of a parallelogram bisect each other) y + 7 = 20

โ y = 20 โ 7 = 13 and,

x + y = 16

โ x + 13 = 16

โ x = 16 โ 13 = 3

x = 3 and y = 13

**9. In the above figure both RISK and CLUE are parallelograms. Find the value of x.**

Solution:

โ K + โ R = 180ยฐ (adjacent angles of a parallelogram are supplementary)

โ 120ยฐ + โ R = 180ยฐ

โ โ R = 180ยฐ โ 120ยฐ = 60ยฐ

also, โ R = โ SIL (corresponding angles)

โ โ SIL = 60ยฐ

also, โ ECR = โ L = 70ยฐ (corresponding angles) x + 60ยฐ + 70ยฐ = 180ยฐ (angle sum of a triangle)

โ x + 130ยฐ = 180ยฐ

โ x = 180ยฐ โ 130ยฐ = 50ยฐ

**10. Explain how this figure is a trapezium. Which of its two sides are parallel? (Fig 3.32)**

Solution:

When a transversal line intersects two lines in such a way that the sum of the adjacent angles on the same side of transversal is 180ยฐ then the lines are parallel to each other. Here, โ M + โ L = 100ยฐ + 80ยฐ = 180ยฐ

Thus, MN || LK

As the quadrilateral KLMN has one pair of parallel line therefore it is a trapezium. MN and LK are parallel lines.

**11. Find mโ C in Fig 3.33 if AB || DC ?**

Solution:

mโ C + mโ B = 180ยฐ (angles on the same side of transversal)

โ mโ C + 120ยฐ = 180ยฐ

โ mโ C = 180ยฐ- 120ยฐ = 60ยฐ

**12. Find the measure of โ P and โ S if SP || RQ ? in Fig 3.34. (If you find mโ R, is there more than one**

**method to find mโ P?)**

Solution:

โ P + โ Q = 180ยฐ (angles on the same side of transversal)

โ โ P + 130ยฐ = 180ยฐ

โ โ P = 180ยฐ โ 130ยฐ = 50ยฐ

also, โ R + โ S = 180ยฐ (angles on the same side of transversal)

โ 90ยฐ + โ S = 180ยฐ

โ โ S = 180ยฐ โ 90ยฐ = 90ยฐ

Thus, โ P = 50ยฐ and โ S = 90ยฐ

Yes, there are more than one method to find mโ P.

PQRS is a quadrilateral. Sum of measures of all angles is 360ยฐ.

Since, we know the measurement of โ Q, โ R and โ S.

โ Q = 130ยฐ, โ R = 90ยฐ and โ S = 90ยฐ

โ P + 130ยฐ + 90ยฐ + 90ยฐ = 360ยฐ

โ โ P + 310ยฐ = 360ยฐ

โ โ P = 360ยฐ โ 310ยฐ = 50ยฐ

## Exercise 3.4 Page: 55

**1. State whether True or False.**

**(a) All rectangles are squares.**

**(b) All rhombuses are parallelograms.**

**(c) All squares are rhombuses and also rectangles.**

**(d) All squares are not parallelograms.**

**(e) All kites are rhombuses.**

**(f) All rhombuses are kites.**

**(g) All parallelograms are trapeziums.**

**(h) All squares are trapeziums.**

Solution:

(a) False.

Because, all square are rectangles but all rectangles are not square.

(b) True

(c) True

(d) False.

Because, all squares are parallelograms as opposite sides are parallel and opposite angles are equal.

(e) False.

Because, for example, a length of the sides of a kite are not of same length.

(f) True

(g) True

(h) True

**2. Identify all the quadrilaterals that have.**

**(a) four sides of equal length (b) four right angles**

Solution:

(a) Rhombus and square have all four sides of equal length.

(b) Square and rectangle have four right angles.

**3. Explain how a square is.**

**(i) a quadrilateral (ii) a parallelogram (iii) a rhombus (iv) a rectangle **Solution

(i) Square is a quadrilateral because it has four sides.

(ii) Square is a parallelogram because itโs opposite sides are parallel and opposite angles are equal.

(iii) Square is a rhombus because all the four sides are of equal length and diagonals bisect at right angles.

(iv)Square is a rectangle because each interior angle, of the square, is 90ยฐ

**4. Name the quadrilaterals whose diagonals.**

**(i) bisect each other (ii) are perpendicular bisectors of each other (iii) are equal **Solution

(i) Parallelogram, Rhombus, Square and Rectangle

(ii) Rhombus and Square

(iii)Rectangle and Square

**5. Explain why a rectangle is a convex quadrilateral. Solution**

Rectangle is a convex quadrilateral because both of its diagonals lie inside the rectangle.

**6. ABC is a right-angled triangle and O is the mid-point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you).**

Solution

AD and DC are drawn so that AD || BC and AB || DC

AD = BC and AB = DC

ABCD is a rectangle as opposite sides are equal and parallel to each other and all the

interior angles are of 90ยฐ.

In a rectangle, diagonals are of equal length and also bisects each other.

Hence, AO = OC = BO = OD

Thus, O is equidistant from A, B and C.

**NCERT Solutions for Class 8 Maths Chapter 3- Understanding Quadrilaterals**

The major concepts covered in this chapter includes: 3.1 Introduction 3.2 Polygons 3.2.1 Classification of Polygons 3.2.2 Diagonals 3.2.3 Convex and Concave Polygons 3.2.4 Regular and Irregular Polygons 3.2.5 Angle sum property 3.3 Sum of the Measures of the Exterior Angles of a Polygon 3.4 Kinds of Quadrilaterals 3.4.1 Trapezium 3.4.2 Kite 3.4.3 Parallelogram 3.4.4 Elements of a parallelogram 3.4.5 Angles of parallelogram 3.4.6 Diagonals of a parallelogram 3.5 Some special parallelograms 3.5.1 Rhombus 3.5.2 A rectangle 3.5.3 A square

Exercise 3.1 Solutions 7 Questions (1 Long Answer Questions, 6 Short Answer Questions)

Exercise 3.2 Solutions 6 Questions (6 Short Answer Questions)

Exercise 3.3 Solutions 12 Questions (6 Long Answer Questions, 6 Short Answer Questions)

Exercise 3.4 Solutions 6 Questions (1 Long Answer Questions, 5 Short Answer Questions)

**NCERT Solutions for Class 8 Maths Chapter 3- Understanding Quadrilaterals**

The Chapter 3 of NCERT Solutions for Class 8 Maths helps you understand the fundamental concepts related to quadrilaterals. From explanation of quadrilaterals to different types of quadrilaterals, the chapter mainly discusses the following concepts:**1.** Parallelogram: A quadrilateral with each pair of opposite sides parallel.**Properties:** Opposite sides are equal. Opposite angles are equal. Diagonals bisect one another**2.** Rhombus: A parallelogram with sides of equal length.**Properties:** All the properties of a parallelogram. Diagonals are perpendicular to each other**3.** Rectangle: A parallelogram with a right angle.**Properties:** All the properties of a parallelogram. Each of the angles is a right angle. Diagonals are equal.**4.** Square: A rectangle with sides of equal length.**Properties:** All the properties of a parallelogram, rhombus and a rectangle.**5.** Kite: A quadrilateral with exactly two pairs of equal consecutive sides**Properties:** The diagonals are perpendicular to one another One of the diagonals bisects the other. Learning the chapter Understanding Quadrilaterals enables the students to:

- Understand the:
- Properties of quadrilaterals: Sum of angles of a quadrilateral is equal to 360
^{o} - Properties of parallelogram: Opposite sides of a parallelogram are equal, Opposite angles of a parallelogram are equal.
- Diagonals of a parallelogram bisect each other.
- Diagonals of a rectangle are equal and bisect each other.
- Diagonals of a rhombus bisect each other at right angles.
- Diagonals of a square are equal and bisect each other at right angles.

- Properties of quadrilaterals: Sum of angles of a quadrilateral is equal to 360

## Frequently Asked Questions on NCERT Solutions for Class 8 Maths Chapter 3

### What kind of questions are present in NCERT Solutions for Class 8 Maths Chapter 3?

NCERT Solutions for Class 8 Maths Chapter 3 has exercises that is

1. Exercise 3.1 with 7 Questions having 1 Long Answer Questions, 6 Short Answer Questions

2. Exercise 3.2 with 6 Questions having 6 Short Answer Questions

3. Exercise 3.3 with 12 Questions having 6 Long Answer Questions, 6 Short Answer Questions

4. Exercise 3.4 with 6 Questions having 1 Long Answer Questions, 5 Short Answer Questions

### What is the meaning of quadrilaterals according to NCERT Solutions for Class 8 Maths Chapter 3?

According to NCERT Solutions for Class 8 Maths Chapter 3, a quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices. Quadrilaterals will typically be of standard shapes with four sides like rectangle, square, trapezoid, and kite or irregular and uncharacterized shapes.

### What are the main topics covered in NCERT Solutions for Class 8 Maths Chapter 3?

The major concepts covered in this chapter includes: 3.1 Introduction 3.2 Polygons 3.2.1 Classification of Polygons 3.2.2 Diagonals 3.2.3 Convex and Concave Polygons 3.2.4 Regular and Irregular Polygons 3.2.5 Angle sum property 3.3 Sum of the Measures of the Exterior Angles of a Polygon 3.4 Kinds of Quadrilaterals 3.4.1 Trapezium 3.4.2 Kite 3.4.3 Parallelogram 3.4.4 Elements of a parallelogram 3.4.5 Angles of parallelogram 3.4.6 Diagonals of a parallelogram 3.5 Some special parallelograms 3.5.1 Rhombus 3.5.2 A rectangle 3.5.3 A square.