# RD Sharma Chapter 7 Class 9 Maths Exercise 7.1 Solutions

RD Sharma Chapter 7 Class 9 Maths Exercise 7.1 Solutions is based on the Introduction to Euclid’s Geometry. Students will learn about the fundamental concepts of geometry like- line, plane, and points in this exercise. We will discuss the Topics and Subtopics include illustration in this exercise on the topics like- Line Segment, Intersecting Lines, Half-Plane, Parallel Lines, Interior Point of a line segment, Distance between two points, etc. Apart from these subtopics, students will get to know about the Axioms (The Fundamental facts, which are taken for granted, without facts, are called axioms).

Find the RD Sharma Chapter 7 Class 9 Maths Exercise 7.1 Solutions PDF with this article, which helps students practice for the exam and get to know about various types of questions related to Euclid’s Geometry. The questions are taken from the CBSE Class 9 and RD Sharma. By practicing these problems rigorously, one can able to apprehend the concepts completely.

## Download RD Sharma Chapter 7 Class 9 Maths Exercise 7.1 Solutions PDF

Solutions for Class 9 Maths Chapter 7 Introduction to Euclid’s Geometry Exercise 7.1

## Important Definition RD Sharma Chapter 7 Class 9 Maths Exercise 7.1 Solutions

Please have a look at the points we have mentioned below. We have provided illustrations about all the RD Sharma Chapter 7 Class 9 Maths Exercise 7.1 Solutions with topics and subtopics related to the Introduction to Euclid’s Geometry. The list of the topics are-

1. Axioms
2. Halves of equality are equal.
3. Three basic concepts in geometry, namely,- line, point, and plane
4. Properties of point and lines
5. Parallel Lines
6. Intersecting Lines
7. Line segment
8. Interior point of a line segment
9. Congruence of line segments
10. Length axioms of a line segment
11. Line segment length axiom, congruent line segment length axiom, Line segment construction axiom
12. Distance between two points
13. Mid-point of a line segment
14. Ray, Half-line, line separation
15. Half-Plane

### Axioms

The term axiom is applied in two related but perceptible senses: “logical axioms” and “non-logical axioms.”

### Halves of equal are equal

Equal means the elements have to be of the same size. Each element is called a half. Two halves equal to one whole.

Suppose a>b & b>c then a>c.

The whole is equal to the sum of its elements and greater than any of its elements.

### Line, Point, and Plane

1. Line- A line is interpreted as a line of points that continues infinitely in two directions. It has only one dimension, length. Points, which are on the equivalent line are known as the collinear points,
2. Points- A point in geometry is a position. It has no size means- no width, no length, and no depth. A point is shown with a dot.
3. Plane- A plane continues infinitely in two dimensions. It has no thickness. The coordinate plane is an example of a Plane. It is identified by three points in the plane that are not on the same line.

### Parallel Lines

Parallel lines do not meet each other. Two straight lines in a plane that don’t intersect at any point are said to be parallel.

The symbol for “parallel to” is //.

### Intersecting Lines

When two or more lines meet each other in a plane, they are known as intersecting lines. The intersecting lines share a basic point, which endures on all the intersecting lines, and is known as the point of intersection.

### Line Segment

A line segment has two endpoints in line. The length of the line segment is set, which is the distance between two fixed points. Here, the length is measured by metric units such as centimeters (cm), millimeters (mm), or by conventional units like- feet or inches.

#### Interior Point of a Line Segment

Suppose the line segment is AB (endpoints are A and B). Then, the points lying in between A and B, excluding the points A and B, are known as Interior Point of a Line Segment.

#### Congruence of Line Segments

Two line segments are supposed to be congruent to each other if they have the same lengths. They may or may not join at the equivalent angle with an axis or point in the plane.

If the two ends of the two-line segments lie on one another, they are congruent.

### Distance Between Two Points

When we comprehend the horizontal and vertical distances between two points, we can calculate the straight line distance like this:

distance = √a² + b²

### Mid-Point of a Line Segment

The midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid of both of the sections and the endpoints. It bisects the section. In simple words, the midpoint is halfway between the two endpoints of the line.

### Half-Plane

A half-plane is a planar area consisting of all points on one side of an endless straight line & no points on the other side. If the points on the line are composed, then it is called a closed half-plane.