## Theorem 10.8 class 9

NCERT Solutions Class 9 Chapter 8 provides students with tricks and techniques to solve the problem in abstract and easier methods, helping the students master the skill of critical thinking and problem-solving at their early stages. An established support system like Vedantu's Free Download NCERT Solutions Class 9 Maths at their early stage of education strengthens their reasoning and logical abilities paving the way to great heights in the field of Mathematics. Chapter 1 - Number System.

Chapter 2 - Polynomials. Chapter 3 - Coordinate Geometry. Chapter 4 - Linear Equations in Two Variables. Chapter 5 - Introductions to Euclids Geometry. Chapter 6 - Lines and Angles. Chapter 7 - Triangles.

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Chapter 8 - Quadrilaterals. Chapter 9 - Areas of Parallelogram and Triangles. Chapter 10 - Circles. Chapter 11 - Constructions.

Chapter 12 - Herons formula. Chapter 13 - Surface area and Volumes. Chapter 14 - Statistics. Chapter 15 - Probability. The solutions provided by the resource people of Vedantu covers the important fundamentals of the angles, diagonals relations of the respective quadrilateral. Section 1 is an introduction to the quadrilateral, and some of its general properties are introduced.

Section 2 is the introduction to types of quadrilateral and their properties. Section 4 includes mainly the Mid-point theorem and its wide range of applications.

A figure formed by joining four non-collinear points is called a quadrilateral. In other words, it is a four-sided polygon. It has four sides and four vertices.The length of each side of a rhombus is 10cm and one of its diagonal is of length 16cm.

The Length of the other Diagonal is: a 18cm b 12cm c 15cm d 16cm. Find the length of each side of the Parallelogram? If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram. Given a triangular prism, then what can we conclude about the lateral faces? Angles of a quadrilateral are in the ratio 3 : 6 : 8: You have to finish following quiz, to start this quiz:.

You have reached 0 of 0 points, 0. The Length of the other Diagonal is:. Firstly we know that diagonal of rhombus bisects each other. Find the angles of the Parallelogram.

In a triangular prism, the bases are triangles and the lateral faces are parallelograms.

Angle Subtended by Arcs (Theorem 1) - Circles - Class 9 Maths

Thus it can be both rectangles and parallelograms. So, option 2 is correct. If the faces are rectangles, then we call it as right triangular prism Observe the following figure. It is clear that the faces of the above figure are rectangles and hence it is right triangular prism. Class 9 Quadrilaterals Quiz - 1 Time limit: 0. Quiz-summary 0 of 10 questions completed Questions: 1 2 3 4 5 6 7 8 9 You have already completed the quiz before.

### Theorem 10.9 - Chapter 10 Class 9 Circles

Question 1 of Correct Firstly we know that diagonal of rhombus bisects each other. Incorrect Firstly we know that diagonal of rhombus bisects each other. Correct In a triangular prism, the bases are triangles and the lateral faces are parallelograms. Incorrect In a triangular prism, the bases are triangles and the lateral faces are parallelograms.

Find angles C and D of the Trapezium. The largest angle is :. Question The length of each side of a rhombus is 10cm and one of its diagonal is of length 16cm.

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The Length of the other Diagonal is: 18cm 12cm 15cm 16cm Correct Firstly we know that diagonal of rhombus bisects each other. Question If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram.

Question Given a triangular prism, then what can we conclude about the lateral faces? Faces are Prism Faces are Parallelogram Faces are Trapezium Faces are rectangle Correct In a triangular prism, the bases are triangles and the lateral faces are parallelograms.

Question 8 of 10 8.Chapter 1 - Number System. Chapter 2 - Polynomials. Chapter 3 - Coordinate Geometry. Chapter 4 - Linear Equations in Two Variables. Chapter 6 - Lines and Angles. Chapter 7 - Triangles. Chapter 8 - Quadrilaterals.

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Chapter 9 - Areas of Parallelogram and Triangles. Chapter 10 - Circles. Chapter 11 - Constructions. Chapter 12 - Herons formula. Chapter 13 - Surface area and Volumes. Chapter 14 - Statistics. Chapter 15 - Probability. This helps the students to get rid of bothering about internet connections. This can be stored as a soft copy as well as a hard copy for Future. Well-experienced mathematics teachers prepared these materials as per the latest curriculum.

Exercise To understand the figure of a circle, we can see many things like a wall clock, wheels of the vehicle, buttons of your shirt, fruits like oranges, coins, CDs, etc.

In this section, NCERT Solutions of Chapter 10 Maths Class 9 defines circle as, The collection of every point in a plane, which is at a fixed distance from a fixed point in the plane, is known as a circle. The entire circle is divided into two - inside of the circle is the interior region and outside of the circle is the exterior region. If you're lying down inside the circle by touching two points of its surface, it is called a chord.

If the chord cuts the second into two halves exactly, then it is known as diameter. The longest chord in the circle is equal to the diameter. Another related term to the circle is the sector.

Students can refer to class 9 chapter 10 maths to get a better understanding of this section. Students are asked to draw a card in a circle. Then extend that line to another point which joins two line segments. It forms a triangle inside the circle. This is known as an angle subtended by a chord at a point. Based on these two theorems were explained in the PDF. If the lengths of chords are the same, then their angles are the same and vice versa. In this section, students can learn about the perpendicular drawn from the centre of the chord by making an activity.The longest side of the triangle is called the "hypotenuse", so the formal definition is:.

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In a right angled triangle: the square of the hypotenuse is equal to the sum of the squares of the other two sides. If we know the lengths of two sides of a right angled triangle, we can find the length of the third side. But remember it only works on right angled triangles! Then we use algebra to find any missing value, as in these examples:. Here is one of the oldest proofs that the square on the long side has the same area as the other squares.

We also have a proof by adding up the areas. Hide Ads About Ads. Example: A "3,4,5" triangle has a right angle in it. Example: Solve this triangle.

Example: What is the diagonal distance across a square of size 1?

## Theorem 10.1 - Chapter 10 Class 9 Circles

Example: Does this triangle have a Right Angle? Yes, it does have a Right Angle! Example: Does an 8, 15, 16 triangle have a Right Angle? Historical Note: while we call it Pythagoras' Theorem, it was also known by Indian, Greek, Chinese and Babylonian mathematicians well before he lived!Candidates who are ambitious to qualify the Class 9 with good score can check this article for Notes.

To assist you with that, we are here with notes. Hope these notes will helps you understand the important topics and remember the key points for exam point of view. Below we provided the Notes of Class 9 Maths for topic Circles. Candidates who are pursuing in Class 9 are advised to revise the notes from this post. With the help of Notes, candidates can plan their Strategy for particular weaker section of the subject and study hard.

The collection of all the points in a plane, which are at a fixed distance from a fixed point in the plane, is called a circle.

A circle is a closed curve all of whose points lie in the same plane and are at the same distance from the centre. The fixed point is called the centre of the circle and the fixed distance is called the radius of the circle.

A circle divides the plane on which it lies into three parts. They are i inside the circle, which is also called the interior of the circle. A chord of a circle is a line joining two points of the circumference. A chord passes through the centre is called diameter. A piece of a circle between two points is called an arc. In a circle equal chords have equal arcs. The region between an arc and the two radii, joining the centre to the end points of the arc is called a sector. When two arcs are equal, that is, each is a semicircle, then both segments and both sectors become the same and each is known as a semicircular region.

### Theorem 10.10 - Chapter 10 Class 9 Circles

Number systems. Irrational numbers : Number systems Real numbers and their decimal expansions : Number systems Operations on real numbers : Number systems.

Simplifying expressions : Number systems Laws of exponents for real numbers : Number systems.

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Polynomials in one variable : Polynomials Zeroes of a polynomial : Polynomials Remainder theorem : Polynomials. Factorisation of polynomials : Polynomials Multiplying polynomials : Polynomials Standard identities : Polynomials Algebraic identities : Polynomials. Coordinate geometry. Cartesian system : Coordinate geometry Plotting points on cartesian plane : Coordinate geometry.

Linear equations in two variables. Solutions of a linear equation : Linear equations in two variables Graph of a linear equation in two variables : Linear equations in two variables. Lines and angles. Pairs of angles : Lines and angles Parallel lines and a transversal : Lines and angles Lines parallel to the same line : Lines and angles.

Angle sum property of a triangle : Lines and angles Proofs: Lines and angles : Lines and angles. Triangles review : Triangles Pythagorean theorem : Triangles Criteria for congruence of triangles : Triangles. Proofs: Triangles : Triangles Inequalities in a triangle : Triangles. Proofs: Kite : Quadrilaterals. Areas of parallelograms and triangles. Area of a parallelogram : Areas of parallelograms and triangles Area of a triangle : Areas of parallelograms and triangles.

Cyclic quadrilaterals : Circles Inscribed shapes problem solving : Circles. Surface areas and volumes. Heron's formula : Surface areas and volumes Cube, cuboid, and cylinder : Surface areas and volumes Cones and spheres : Surface areas and volumes. Bar graphs : Statistics Histograms : Statistics Mean. Experimental probability : Probability Probability problems : Probability. Course challenge. Community questions.We know that the chord of a circle is a line segment having its endpoints on the circumference of the circle.

There can be several chords of the same or different lengths in a circle. Observe, for example, two unequal chords of a circle with centre O.

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In the circle, chord CD is longer than chord AB. Note the angles subtended by the chords at the centre. While AB subtends an acute angle i. Thus, in a circle, chords of different lengths subtend different angles at the centre. On the other hand, equal or congruent chords subtend equal or congruent angles at the centre. This is a very useful property of circle. In this lesson, we will learn more about this property and solve some examples based on the same.

We know that the most important point required to draw a circle is its centre which is equidistant from all other points lying on the boundary of the circle. We can also draw infinitely many circles of different radii with the same centre.

Now, let us observe some points shared by circles on their boundaries. A few circles passing through common points X, Y and Z are shown below. It can be observed that when point X is taken alone, we can draw infinitely many circles passing through it. Similarly, when X and Y are taken together, we can get infinitely many circles passing through them. However, when we take the three points X, Y and Z together, we obtain only one circle passing through them. Thus, we can conclude that to draw a unique circle, we require at least three non-collinear points.

In this lesson, we will study more about this conclusion. Now, the property that relates these perpendicular distances of equal chords is stated as follows:. So, according to this property, since AB is equal to CD, their distances from the centre are also equal, i.