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## NCERT Class 7 Maths Textbook Chapter 10 With Answer PDF Free Download

### Chapter 10: Practical Geometry

The concepts covered in this chapter include:

- Construction of a Line Parallel To a Given Line, Through a Point Not on The Line
- Construction of Triangle
- Constructing a Triangle When the Lengths of its Three Sides are Known (SSS Criterion)
- Constructing a Triangle When the Lengths of Two Sides And The Measure of The Angle Between Them Are Known (SAS Criterion)
- Constructing a Triangle When The Measures of Two of Its Angles and The Length of The Side Inclined Between Them Is Given (ASA Criterion)
- Constructing a Right-Angled Triangle When The Length of One Leg and Its Hypotenuse are Given (RHS Criterion)

#### 10.1 INTRODUCTION

You are familiar with a number of shapes. You learned how to draw some of them in the earlier classes.

For example, you can draw a line segment of a given length, a line perpendicular to a given line segment, an angle, an angle bisector, a circle, etc. Now, you will learn how to draw parallel lines and some types of triangles

#### 10.3 CONSTRUCTION OF TRIANGLES

It is better for you to go through this section after recalling ideas on triangles, in particular, the chapters on properties of triangles and the congruence of triangles.

You know how triangles are classified based on sides or angles and the following important properties concerning triangles:

(i) The exterior angle of a triangle is equal in measure to the sum of interior opposite angles.

(ii) The total measure of the three angles of a triangle is 180°.

(iii) Sum of the lengths of any two sides of a triangle is greater than the length of the third side.

(iv) In any right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In the chapter on ‘Congruence of Triangles’, we saw that a triangle can be drawn if any one of the following sets of measurements is given:

(i) Three sides.

(ii) Two sides and the angle between them.

(iii) Two angles and the side between them.

(iv) The hypotenuse and a leg in the case of a right-angled triangle.

We will now attempt to use these ideas to construct triangles.

Author | NCERT |

Language | English |

No. of Pages | 12 |

PDF Size | 1.4 MB |

Category | Education |

Source/ Credits | ncert.nic.in |

### NCERT Solutions Class 7 Maths Chapter 10 Practical Geometry

**Ex 10.1 Class 7 Maths Question 1.**Draw a line, say AB, take a point C outside it. Through C draw a line parallel to AB using a ruler and compasses only.

Solution:

Steps of construction:

(i) Draw a line AB.

(ii) Take any point D on it.

(iii) Join the given point C to D and mark ∠1 to ∠CDB.

(iv) Mark ∠1 = ∠2 at C and produce to both side.

(v) MN is the required line.

Using the Property of Alternate Angles

Ex 10.1 Class 7 Maths Question 2.

Draw a line Z. Draw a perpendicular to l at any point on l. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

Solution: ‘Steps of construction:

(i) Draw a given line Z and take any point P on it.

(ii) Draw a perpendicular line at P to line Z such that PX = 4 cm.

(iii) Draw ∠2 = ∠1 i.e. 90° at PX and produce the line on both sides.

(iv) m is the required line parallel to Z through X.

Using Properties of Alternate Angles

NCERT Class 7 Maths Textbook Chapter 10 With Answer PDF Free Download