• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

  • NCERT Solutions
    • NCERT Solutions for Class 12 English Flamingo and Vistas
    • NCERT Solutions for Class 11 English
    • NCERT Solutions for Class 11 Hindi
    • NCERT Solutions for Class 12 Hindi
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
    • Wordfeud Cheat
  • MCQ Questions

Verify that the Opposite Angles of a Cyclic Quadrilateral Experiment Class 9 Maths Practical NCERT

The experiment to determine Verify that the Opposite Angles of a Cyclic Quadrilateral are part of the Class 9 Maths Lab Manual provides practical activities and experiments to help students understand mathematical concepts effectively. It encourages interactive learning by linking theoretical knowledge to real-life applications, making mathematics enjoyable and meaningful.

Maths Lab Manual Class 9 CBSE Verify that the Opposite Angles of a Cyclic Quadrilateral Experiment

Determine Verify that the Opposite Angles of a Cyclic Quadrilateral Class 9 Practical

OBJECTIVE

To verify that the opposite angles of a cyclic quadrilateral are supplementary.

Materials Required

  1. Cardboard
  2. White paper
  3. Drawing sheet
  4. Geometry box
  5. Scissors
  6. Sketch pens
  7. Adhesive
  8. Transparent sheet

Prerequisite Knowledge

  1. Knowledge about the supplementary angles, linear pair axiom and interior opposite angles.
  2. All the basic information related to cyclic quadrilateral.

Theory

  1. Two angles are said to be supplementary, if the sum of their measures is 180°. In the figure given below, ∠BOC and ∠AOC are supplementary angles, (see Fig. 25.1)
    NCERT Class 9 Maths Lab Manual - Verify that the Opposite Angles of a Cyclic Quadrilateral 1
  2. If a ray stands on a line, then the sum of two adjacent angles so formed is 180°, i.e. the sum of the linear pair is 180°.
    In the above figure, ∠AOC + ∠BOC =180°.
    NCERT Class 9 Maths Lab Manual - Verify that the Opposite Angles of a Cyclic Quadrilateral 2
    If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line or two opposite rays. The two axioms given above together are called the linear pair axiom.
  3. If the side BC of ΔABC is produced to D, then ∠AÇD is called an exterior angle of ΔABC at C, while ∠BAC and ∠ABC are called its interior opposite angles. It is denoted by exterior ∠ACD.
    NCERT Class 9 Maths Lab Manual - Verify that the Opposite Angles of a Cyclic Quadrilateral 3
  4. A quadrilateral ABCD is called a cyclic quadrilateral, if all the four vertices A B, C and D are concyclic, i.e. A, B, C and D lie on a circle. In Fig. 25.4, ABCD is a cyclic quadrilateral. The sum of opposite angles of a cyclic quadrilateral is always 80°, i.e. they are supplementary.
    NCERT Class 9 Maths Lab Manual - Verify that the Opposite Angles of a Cyclic Quadrilateral 4

Procedure

  1. Take a cardboard of suitable size and paste a white paper on it.
  2. Draw a circle of suitable radius on drawing sheet.
  3. Cut out the circle and paste it on cardboard.
  4. In the circle, draw a quadrilateral ABCD such that all the four vertices of quadrilateral lie on the circle. Name the angles as ∠A, ∠B, ∠C and ∠D. (see Fig. 25.5)
    NCERT Class 9 Maths Lab Manual - Verify that the Opposite Angles of a Cyclic Quadrilateral 5
  5. Make the cut outs of the angles, (i.e. ∠A, ∠B, ∠C and ∠D) with the help of a transparent sheet, (see Fig. 25.6)
    NCERT Class 9 Maths Lab Manual - Verify that the Opposite Angles of a Cyclic Quadrilateral 6
  6. By using adhesive, paste cut outs of the opposite angles ∠A and ∠C, ∠B and ∠D. (see Fig. 25.7)
    NCERT Class 9 Maths Lab Manual - Verify that the Opposite Angles of a Cyclic Quadrilateral 7

Demonstration
Joining the opposite angles ∠A and  ∠C, ∠B and ∠D, we get straight angles, (see Fig. 25.4)
Hence, ∠A + ∠C = 180° and ∠B + ∠D = 180°.

Observation
By actual measurement,  ∠A = ……… , ∠B = ……… ,
∠C = ……… ,  ∠D = ……… ,
So, ∠A + ∠C = ……… , ∠B + ∠D = ……… .
Hence, sum of each pair of the opposite angles of a cyclic quadrilateral is ……… .

Result
We have verified that the opposite angles of a cyclic quadrilateral are always supplementary.

Application
This property can be used in solving various problems in geometry.

Viva Voce
Question 1:
What do you understand by the term a cyclic quadrilateral?
Answer:
A quadrilateral having all the vertices on the boundary of the circle is called a cyclic quadrilateral.

Question 2:
What is the sum of each pair of opposite angles of a cyclic quadrilateral?
Answer:
180°

Question 3:
If one of the angles of a cyclic quadrilateral is 40°, then what will be the value of its opposite angle?
Answer:
140°

Question 4:
If a cyclic quadrilateral is a parallelogram, then what is the type of parallelogram?
Answer:
Rectangle

Question 5:
Is the sum of adjacent angles of a cyclic quadrilateral 180°?
Answer:
No, only the sum of opposite angles of a cyclic quadrilateral is 180°.

Question 6:
What is the name of quadrilateral, if each pair of opposite angles is supplementary?
Answer:
Cyclic quadrilateral

Question 7:
What is the type of quadrilateral formed by the internal angle bisectors of cyclic .quadrilateral?
Answer:
Cyclic quadrilateral

Question 8:
Which property has to be added in a trapezium for making it a cyclic quadrilateral?
Answer:
Non-parallel sides of a trapezium should be equal.

Suggested Activity
Verify that the exterior angle of a cyclic quadrilateral is equal to the opposite interior angle.

Math LabsMath Labs with ActivityMath Lab ManualScience LabsScience Practical Skills

NCERT Class 9 Maths Lab Manual 

  • Determine Verify that the Sum of the Angles of a Quadrilateral is 360° Class 9 Experiment
  • Determine Find the Formula for the Area of a Trapezium Class 9 Experiment
  • Determine Verify that the Parallelograms on the Same Base Class 9 Experiment
  • Determine Verify that the Triangles on the Same Base Class 9 Experiment
  • Determine Verify that the Ratio of the Areas of a Parallelogram Class 9 Experiment
  • Determine Verify that the Angle Subtended by an Arc of a Circle Class 9 Experiment
  • Determine Verify that the Angles in the Same Segment of a Circle are Equal Class 9 Experiment
  • Determine Verify that the Opposite Angles of a Cyclic Quadrilateral Class 9 Experiment
  • Determine Form a Cube and Find the Formula for its Surface Class 9 Experiment
  • Determine Form a Cuboid and Find the Formula for its Surface Area Class 9 Experiment
  • Determine Form a Cone from a Sector of a Circle Class 9 Experiment
  • Determine Find a Formula for the Curved Surface Area of a Cylinder Class 9 Experiment
  • Determine Find the Relationship among the Volumes of a Cone Class 9 Experiment
  • Determine Obtain the Formula for the Surface Area of a Sphere Class 9 Experiment
  • Determine Draw Histograms for Classes of Equal Widths and Varying Widths Class 9 Experiment
  • Determine Find Probability of Unit’s Digit of Telephone Numbers Class 9 Experiment
  • Determine Find Probability of each Outcome or a Die Class 9 Experiment

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers
  • The Summer Of The Beautiful White Horse Answers
  • Job Application Letter class 12 Samples
  • Science Lab Manual Class 9
  • Letter to The Editor Class 12 Samples
  • Unseen Passage For Class 6 Answers
  • NCERT Solutions for Class 12 Hindi Core
  • Invitation and Replies Class 12 Examples
  • Advertisement Writing Class 11 Examples
  • Lab Manual Class 10 Science

Recent Posts

  • Understanding Diversity Question Answer Class 6 Social Science Civics Chapter 1 NCERT Solutions
  • Our Changing Earth Question Answer Class 7 Social Science Geography Chapter 3 NCERT Solutions
  • Inside Our Earth Question Answer Class 7 Social Science Geography Chapter 2 NCERT Solutions
  • Rulers and Buildings Question Answer Class 7 Social Science History Chapter 5 NCERT Solutions
  • On Equality Question Answer Class 7 Social Science Civics Chapter 1 NCERT Solutions
  • Role of the Government in Health Question Answer Class 7 Social Science Civics Chapter 2 NCERT Solutions
  • Vital Villages, Thriving Towns Question Answer Class 6 Social Science History Chapter 9 NCERT Solutions
  • New Empires and Kingdoms Question Answer Class 6 Social Science History Chapter 11 NCERT Solutions
  • The Delhi Sultans Question Answer Class 7 Social Science History Chapter 3 NCERT Solutions
  • The Mughal Empire Question Answer Class 7 Social Science History Chapter 4 NCERT Solutions
  • India: Climate Vegetation and Wildlife Question Answer Class 6 Social Science Geography Chapter 8 NCERT Solutions
  • Traders, Kings and Pilgrims Question Answer Class 6 Social Science History Chapter 10 NCERT Solutions
  • Environment Question Answer Class 7 Social Science Geography Chapter 1 NCERT Solutions
  • Understanding Advertising Question Answer Class 7 Social Science Civics Chapter 7 NCERT Solutions
  • The Making of Regional Cultures Question Answer Class 7 Social Science History Chapter 9 NCERT Solutions

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions