# Geometry

## Introduction to Euclid’s Geometry Class 9th

Euclid’s Definitions, Axioms, and Postulates Euclid listed 23 definitions in book 1 of the ‘Elements’. A few of them are given below : Euclid gave some certain properties which were assumed by him and which were not proved. Actually, these assumptions were ‘obvious universal truths’. There were two types of these assumptions: axioms and postulates. …

## The Similarity of Triangles Class 10th

Introduction The triangle is the shape, we are well known about it and its properties. We have studied different triangles and terms related to them like a scalene triangle, equilateral triangle, isosceles triangle, the area of the triangle, the perimeter of a triangle, the median of a triangle, the altitude of the triangle, etc. In …

## Lines and Angles Class 9th

Introduction In the previous classes, we studied line segments, rays, and lines and their properties. We also know the difference between them. Now, we shall study lines and angles, the formation of angles with the help of lines, theorems based on the properties, etc. We also know the importance of lines and angles in our …

## Circumference of Circle Class 10th

Introduction In our daily life, we use many circular objects like rubber rings, bangles, coins, wheels, etc. If we want to measure their circular length then how can we do it? Here’s an activity to understand it clearly. If we have to measure the circular length (Circumference of Circle) of a wheel then we shall …

## Circles Passing Through Different Points Class 10th

Circles Passing Through Different Points are as follows. Circles Passing Through One Point If there is a point in a plane then through that point many circles can pass. We can say infinite circles can pass. We can understand it practically from the figure given below. Circles Passing Through Two Points If there are two …

## Angle Subtended by a Chord of Circle Class 10th

Introduction In a circle, if we draw a chord and join the two ends of the chord to the third point which is situated at the Centre or on the circle, then the angle made at the third point is the angle subtended by the chord of the Circle. In the above figure, ∠PRQ and …

## Tangent and Secant of Circle Class 10th

Introduction Definition of Tangent and Secant of Circle Secant line – In a circle, if a line intersects the circle at two points, then that line is called the secant line of the circle. In the above figures, line PQ is a secant line that intersects the circles at points A and B which are …

## Cyclic Quadrilaterals Class 10th

Introduction Definition – The quadrilaterals whose all four vertices lie on the circle are called Cyclic Quadrilaterals. Here, ABCD is a cyclic quadrilateral. Its vertices A, B, C and D are situated on the circle. If we measure all four angles and add the opposite angles then we will find that sum of opposite angles …

## Circles Class 10th

Introduction Definition – A set of points located at a fixed distance from a fixed point in a plane is called a Circle. The fixed point is called the centre and the fixed distance is called the radius of the circle. Examples – The path of the tip of the second’s hand in the clock, …

## Angles of the Alternate Segment of a Circle Class 10th

Introduction In a circle, if a tangent is drawn then at the point of contact we draw a chord. This chord divides the circle into two segments then the angle made by the chord with the tangent will be equal to the angle made in the alternate segment by the chord. This is the concept …

## Angle Subtended by the Arc of a Circle Class 10th

Introduction We studied the chords in a circle. We take the endpoints of the chord which are on the circle and the circular length of both endpoints is called an Arc. If there are two equal arcs then the angle subtended by both the arcs at the Centre will be equal and if there are …

## Triangle and its Properties Class 10th

Definition A Closed figure made of three line segments is called a Triangle. It has three sides, three angles, and three vertices. Here, Triangle ABC and its Properties are shown below. Three sides – AB, BC, CA Three angles – ∠A, ∠B, ∠C Three vertices – A, B, C Classification of Triangles – ➤ Based on …

## Pythagoras Theorem (Boudhayana Theorem) Class 10th

Introduction The Pythagoras theorem is given by the Greek mathematician Pythagoras. Before Pythagoras, this theorem was discovered by Indian mathematician Boudhayana so this theorem is also known as Boudhayana Theorem. This theorem is also called Pythagorean Theorem. Statement – According to this theorem, In a right-angled triangle, the square of the hypotenuse side is equal …