The document is a lesson transcript for a mathematics class on right angles and circles. It discusses how if the endpoints of a diameter of a circle are joined to any other point on the circle, the angle formed is a right angle. It provides definitions, facts, and concepts to the students. The lesson involves drawing circles and diameters, forming triangles, and proving that the angles are right angles. Students are asked to apply the concept to determine if angles in other drawings are right angles.

1. LESSON TRANSCRIPT
Name of the teacher: Athira R L Standard and Division: X
Name of the school : Strength:
Subject : Mathematics Duration: 40 min
Unit : Circles Date :
Topic :Right angles and circles
Curricular Statements
 Creating the ideas of right angled triangle.
 Applying these ideas in different situation.
Content Analysis
Terms : Right angles, Circle, diameter, Isosceles triangle, radius, Sides, Angles.
Facts : 1. If the two sides of a triangle are equal, then the opposite angles of these sides are equal.
2. A triangle in which two sides are equal is called Isosceles triangle.
3. The sum of the angles of a triangle is 1800.
4. The angle in the semicircle is 900.
Concept : Right angles and circles
Process : If the end points of a diameter of a circle are joined to any other point on the circle, then we
get is a right angle.
Learning Outcomes
Remembering : 1. The student will be able recalls the terms Isosceles triangle, right angle.
2. The student will be able to recognise the facts such as angle in the semicircle is
900.
Understanding : 1. The student will be able to give illustration of terms Isosceles triangle, right
angled triangle.
2. The student will be able to define the concept of right angled triangle in a circle.
Applying : 1. The student will be able to apply the knowledge of angle in a semicircle in the
Familiar situation.

2. 2. The student will be able to judges the adequacy and inadequacy of the data.
Analysing : 1. The student will be able to analyse the concept.
2. the student will be able to justify the terms and concept.
Creating : 1. The student will be able to create the new ideas of this topic.
Skill : The student will able to draw pictures.
The student will be able to handle the geometrical instruments.
Pre-requisites
The student knows about the terms right angles, circle, diameter, Isosceles triangle, radius,
sides, and angles.
Teaching learning resources
 Model of circle
 Geometrical instruments
 Ordinary class room equipment

3. Class Interaction Procedure Pupil’s response
Introduction
Teacher ask questions to the students to testing their
previous knowledge.
1. What is a right angled triangle?
2. Which side is called the hypotenuse?
3. What about an Isosceles triangle?
Teacher shows a model of circle. And also
Teacher tells to the student to draw a circle and also tells to
them to draw a diameter on it.
Teacher also draws it on the board.
Teacher gives name to the diameter.
A B
Teacher tells to the student to join the end points of the
diameter AB to other point P on the Circle.
P
A B
1.A right angled triangle is a triangle with one angle is
900.
2.The longest side of a right angled triangle is called its
hypotenuse.
3. A triangle in which 2 sides are equal.
A B
P
A B

4. What about the <APB?
Is APB a right angled triangle?
How will you find the angle APB?
Presentation
P
A B
In this figure, which is the diameter?
How did we prove that angle P is a right angle?
Here O is the centre of the circle.
P
A > B
Join P and O
P
A B
What you get if P is joining to O?
What are the peculiarities of these triangles?
What we call if the two sides of a triangle are equal?
That is, APO and BPO are isosceles triangle
In APO, Which are the equal sides?
That is, AO = OP
In BPO, Which are the equal sides?
AB is the diameter
P
A B
P
A B
2 triangles
2 sides of these two triangles are equal.
Isosceles triangles.
AO and OP
O
O
O
O

5. That is , OP = OB
If we take < APO = x0 and < BPO = y0,
What about the angles A and B?
P
A B B
That is , if we take < APO = x0 and < BPO = y0 then we
get < A = x0 and <B = y0
P
A B
For what?
What is the sum of the angles of a triangle?
Since the sum of the angle of triangle ABP is 1800.
Then we have,
x + y + (x + y) = 1800
From this we get,
2x + 2y = 1800
Then what we get?
Therefore x + y = 900
From this, What we can understand?
OP and OB
If 2 sides of a triangle are equal then the angles opposite
to these sides are also equal.
1800
x + y+ (x + y) = 1800
2x + 2y = 1800
x + y = 900
X0 y0
O
X0 y0
X0 y0
O

6. Generalisation
We can conclude that,
If the end points of a diameter of a circle are joined to
any other point on the circle, then we get is a right angle.
Application
Class Assignment
L
M N
Is angle MLN a right angle? Give reason.
Join L and O. P
M N
Join L and O P
M N
O
O

7. We get two triangles.
Triangle PMO and triangle PNO.
Have any similarity between these triangles?
These two triangles are not Isosceles triangles.
Therefore these two triangles are not congruent.
So angle MPN is not equal to 900.
We get two triangles.
Triangle PMO and triangle PNO.
There is no similarity between them.
These two triangles are not Isosceles triangles.
Therefore these two triangles are not congruent.
So angle MPN is not equal to 900.
Review
What is the angle in a semicircle?
Home Assignment
If the end points of a diameter of above picture is join to any point inside the circle, then what about the angle inside
the circle?