## NCERT Solutions for Class 8 Chapter 3 Understanding Quadrilaterals -Free PDF Download

Free PDF download of NCERT Solutions Maths Class 8 Solutions Chapter 3 – Understanding Quadrilaterals solved by Expert Maths Teachers on CoolGyan.Org. All Chapter 3 – Understanding Quadrilaterals Questions with Solutions for NCERT to help you to revise complete Syllabus and Score More marks.

Maths Revision Notes for Class 8

Chapter Name | Understanding Quadrilaterals |

Chapter | Chapter 3 |

Exercise | Exercise 3.1 |

Class | Class 8 |

Subject | Maths NCERT Solutions |

Board | CBSE |

TEXTBOOK | CBSE NCERT |

Category | NCERT Solutions |

**NCERT SOLVED**

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

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

**(a) Simple curve **

**(b) Simple closed curve**

**(c) Polygon **

**(d) Convex polygon**

**(e) Concave polygon**

**Ans. **(a) Simple curve

(b) Simple closed curve

(c) Polygons

(d) Convex polygons

(e) Concave polygon

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

**(a) A convex quadrilateral **

**(b) A regular hexagon**

**(c) A triangle**

**Ans. **(a) A convex quadrilateral has two diagonals.

Here, AC and BD are two diagonals.

(b) A regular hexagon has 9 diagonals.

Here, diagonals are AD, AE, BD, BE, FC, FB, AC, EC and FD.

(c) A triangle has no diagonal.

**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)**

**Ans. **Let ABCD is a convex quadrilateral, then we draw a diagonal AC which divides the quadrilateral in two triangles.

A + B + C + D

= 1 + 6 + 5 + 4 + 3 + 2

= (1 + 2 + 3) + (4 + 5 + 6)

=

[By Angle sum property of triangle]

=

Hence, the sum of measures of the triangles of a convex quadrilateral is

Yes, if quadrilateral is not convex then, this property will also be applied.

Let ABCD is a non-convex quadrilateral and join BD, which also divides the quadrilateral in two triangles.

Using angle sum property of triangle,

In ABD, 1 + 2 + 3 = ……….(i)

In BDC, 4 + 5 + 6 = ……….(i)

Adding eq. (i) and (ii),

1 + 2 + 3 + 4 + 5 + 6 =

1 + 2 + (3 + 4) + 5 + 6

=

A + B + C + D =

Hence proved.

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

Figure | ||||

Side | 3 | 4 | 5 | 6 |

Angle sum |

**What can you say about the angle sum of a convex polygon with number of sides?**

**Ans. **(a) When = 7, then

Angle sum of a polygon =

(b) When = 8, then

Angle sum of a polygon =

(c) When = 10, then

Angle sum of a polygon =

(d) When = then

Angle sum of a polygon =

**5. What is a regular polygon? State the name of a regular polygon of:**

**(a) 3 sides **

**(b) 4 sides **

**(c) 6 sides**

**Ans. A regular polygon**: A polygon having all sides of equal length and the interior angles of equal size is known as regular polygon.

(i) 3 sides

Polygon having three sides is called a **triangle**.

(ii) 4 sides

Polygon having four sides is called a **quadrilateral**.

(iii) 6 sides

Polygon having six sides is called a **hexagon**.

**6. Find the angle measures **** in the following figures:**

**Ans. **(a) Using angle sum property of a quadrilateral,

(b) Using angle sum property of a quadrilateral,

(a) First base interior angle

=

Second base interior angle

=

There are 5 sides, = 5

Angle sum of a polygon =

= =

(b) Angle sum of a polygon =

= =

Hence each interior angle is

**7. (a) Find **** **

**(b) Find **

**Ans. **(a) Since sum of linear pair angles is

And

Also

[Exterior angle property]

(b) Using angle sum property of a quadrilateral,

Since sum of linear pair angles is

……….(i)

……….(ii)

……….(iii)

……….(iv)

Adding eq. (i), (ii), (iii) and (iv),