maths period plan

1. DIGITAL PLAN – 1 (36)
Preliminaries
• 1.Name of the Teacher Trainee: Shama Afreen
• 2.Roll Number: 1636-701-056
• 3.Name of the College: Ramadevi College of Education
• 4.Name of the Cooperating School: Little buds high School
• 5.Subject: Mathematics
• 6.Class: IX
• 7.Name of the Lesson: Circles
• 8.Subtopic: Introduction to Circles
• 9.Period No: 36
• 10.Duration: 45 Mins

2. PROBING QUESTIONS
 What is Circle?
What is circumference of Circle?
What is Diameter?

3. ANNOUNCEMENT OF THE TOPIC
Introduction to Circles

4. DEMONSTRATION AND DISCUSSION
• Theorem-1: “The perpendicular from the center of a circle to a chord
bisects the chord”.
Given: A circle with center O. AB and PQ are chords of the circle. AB = PQ
To Prove: ∠AOB = ∠POQ
• Proof: In triangles AOB and POQ,
AB = PQ (Given)
OA = OP (Radii of same circle)
OB = OQ (Radii of same circle)
ΔAOB ≅ ΔPOQ (SSS congruence rule)
⇒ ∠AOB = ∠POQ (Corresponding angles)
• Hence, the theorem is proved.

5. • Theorem-2: “ The perpendicular from the center of a circle to a chord bisects the
chord.”
Given: A circle with center O. AC is a chord and OB ⊥ AC.
To prove: AB = BC.
Construction: Join OA and OC.
Proof: In triangles OBA and OBC,
∠OBA = ∠OBC = 90o (Since OB ⊥ AC)
OA = OC (Radii of the same circle)
OB = OB (Common side)
ΔOBA ≅ ΔOBC (By RHS congruence rule)
⇒ AB = BC (Corresponding sides of congruent triangles)
Thus, OB bisects the chord AC.
• Hence, the theorem is proved.

6. PROBLEM SOLVING
• Q: In the figure, O is the center of the circle. Find the length of CD, if
AB = 5 cm.
• Sol: In AOB and COD
OA=OC (radii)
OB=OD (radii)
AOB = COD
Therefore, AOB = COD
AB = CD
Therefore, if AB=5 cm, then CD=5 cm.

7. CONCLUSION
Today we have learnt about
“ Introduction to Circles”

8. EVALUATION