NCERT Solutions for Class 7 Maths Chapter 10 Exercise 10.1

NCERT Solutions for Class 7 Maths Chapter 10 Exercise 10.1 (Ex. 10.1) Practical Geometry updated for academic session 2020-2021. All the contents are revised for new session 2020-21 following the latest NCERT Books and new CBSE Syllabus.

In class 7 math exercise 10.1, we will learn to draw a parallel line to a given line using ruler and compass. There are only three questions in ex. 10.1 but all the three are important for exams.

Class 7 Maths Chapter 10 Exercise 10.1 Solution

Class: 7Mathematics
Chapter: 10Practical Geometry
Exercise: 10.1Hindi and English Medium

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Construction of Parallel Lines

Two lines are said to be parallel in a plane if they do not intersect if extended till infinite in both the directions. The distance between two lines is similar throughout the whole length. The symbol to denote the parallel lines is ||.
To Draw a Line Parallel to a Given Line and Passing Through a Given Point
Example- 1:
Draw a line parallel to a given line l and passing through a given point P.

Steps of construction:

1. Draw a line AB and mark a point C outside it.
2. Take any point D on AB and join CD.
3. With D as centre, draw an arc cutting AB and DC at N and M respectively.
4. With C as centre and same radius as above, draw an arc to cut DC at P.
5. With P as centre and radius equal to MN, draw an arc cutting the arc drawn in step 4 at R.
6. Join CR and extend it to both directions to get the required parallel line. Line CR is the required line parallel to AB.

Properties of parallel lines:

(i) Interior and exterior alternate angles are equal.
(ii) Corresponding angles are equal.
(iii) Co-interior or allied angles are supplementary. the pair of corresponding angles is equal, then the two straight lines are parallel to each other.

Which other construction is used when constructing parallel lines?

It is called the ‘angle copy method’ because it works by using the fact that a transverse line drawn across two parallel lines creates pairs of equal corresponding angles. It uses this in reverse – by creating two equal corresponding angles, it can create the parallel lines.

How do you prove two lines are parallel?

If two parallel lines are cut by a transversal, then corresponding angles are congruent. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

Can two rays be parallel?

Parallel rays two rays are parallel if the corresponding lines determined by them are parallel. In other word two rays in the same plane are parallel if they do not intersect each other even if extended indefinitely beyond their initial points.

NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry Exercise 10.1