(ii) PQ = SR

(iii) PQRS is a parallelogram.

NCERT Solutions for Class 9 Maths Chapter 8 QUADRILATERALS Exercise 8.2 Question 1. NCERT Questions Exercises

9th Maths Chapter 8 QUADRILATERALS

NCERT Academic Session 2023-2024

CBSE Board and Others state Board

Description:

A quadrilateral is a polygon with four sides and angles. It has four straight sides meeting at four vertices. The sum of its interior angles is always 360 degrees. Types like rectangles, squares, parallelograms, and rhombuses have distinct properties based on side lengths, angles, and parallel sides.

9th Maths Chapter 9 Circles

NCERT Academic Session 2023-2024

CBSE Board and Others state Board

Description:

Two intersecting circles create points where their circumferences meet. Their interaction results in distinct configurations: secants intersecting at two points on both circles, tangents touching at one point internally or externally, and chords crossing within or outside both circles. These intersections offer diverse geometric relationships and configurations based on the circles’ relative positions and sizes.

9th Maths Chapter 9 Circles

NCERT Academic Session 2023-2024

CBSE Board and Others state Board

Description:

Intersecting lines within a circle involve chords, secants, and tangents meeting or crossing at one or more points. Chords link two points on the circle’s circumference, while secants intersect the circle at two points, extending outside. Tangents touch the circle at a single point, forming a right angle with the radius. Analyzing these intersections aids in understanding circle-related geometry and angle relationships.

9th Maths Chapter 9 Circles

NCERT Academic Session 2023-2024

CBSE Board and Others state Board

Description:

Angles within a circle take diverse forms. Central angles, extending from the circle’s center, match the arcs they cover. Inscribed angles, nested within the circle, are half the measure of the arcs they span. Doubling the inscribed angle produces the angle formed at the circle’s center, while halving the intercepted arc creates the angle between a tangent and a chord. These angles serve vital roles in circle geometry, aiding in measurements and spatial relationships.

9th Maths Chapter 9 Circles

NCERT Academic Session 2023-2024

CBSE Board and Others state Board

Description:

In a circle, various angles emerge, such as central angles, originating from the circle’s center and covering arcs. Inscribed angles occur within the circle, halving their intercepted arcs. Additionally, angles at the center double inscribed angles, while the angle between a tangent and chord halves the arc it intercepts. These angles aid in circle-related geometric calculations and relationships.

9th Maths Chapter 9 Circles

NCERT Academic Session 2023-2024

CBSE Board and Others state Board

Description:

An arc in a circle is a curved section between two points on the circle’s circumference. It measures a fraction of the circle’s circumference, expressed in degrees or radians. Arcs vary from minor (under 180°) to major (exceeding 180°) and are vital in geometry for angles and circle-related calculations.

9th Maths Chapter 9 Circles

NCERT Academic Session 2023-2024

CBSE Board and Others state Board

Description:

Concentric circles share a common center and differ in radii. These circles, centered at the same point, form nested rings. They illustrate symmetry and spatial relationships, finding application in geometry, architectural designs, and various fields due to their shared center concept facilitating measurements and pattern formations.

9th Maths Chapter 9 Circles

NCERT Academic Session 2023-2024

CBSE Board and Others state Board

Description:

– A central angle is formed by extending the endpoints of a chord to the center of the circle.

– An inscribed angle is formed by two chords or a chord and a tangent line where the angle’s vertex lies on the circle.

– When chords intersect inside a circle, angles are formed at the point of intersection.

– The angle between a chord and a tangent at the point of contact is half the measure of the intercepted arc on the circle.

These angle relationships are crucial in understanding the geometry of circles and solving problems involving chords, arcs, and angles within circles.

]]>9th Maths Chapter 9 Circles

NCERT Academic Session 2023-2024

CBSE Board and Others state Board

Description:

A chord of a circle is a straight line segment that connects two points on the circumference of the circle. It lies entirely inside the circle and can vary in length and position within the circle. If a chord passes through the center of the circle, it becomes the diameter, which is the longest possible chord for that circle. The perpendicular from the center of the circle to a chord bisects the chord, dividing it into two equal segments. Chords play a fundamental role in circle geometry and are used to establish various relationships within circles. ]]>

Prove to corresponding sides of similar triangles

Class 9, EXERCISE 8.2, Page No: 151, Questions No:5.

Session 2023-2024 are based on CBSE Board. ]]>