Mathematics - Junior Secondary 1 - Angles continued (Theorems)

Angles continued (Theorems)

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TERM: 3RD TERM

WEEK 7
Class: Junior Secondary School 1
Age: 12 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Angles Continued (Theorems)
Focus: Sum of Angles on a Straight Line, Supplementary Angles, Complementary Angles, Sum of Angles of a Triangle

SPECIFIC OBJECTIVES:

By the end of the lesson, pupils should be able to:

  1. Prove that the sum of angles on a straight line is 180°.
  2. Identify and apply supplementary angles.
  3. Identify and apply complementary angles.
  4. Apply the sum of angles of a triangle theorem.
  5. Solve problems involving angles on a straight line, supplementary and complementary angles, and angles of a triangle.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Drills and exercises
  • Real-life application

INSTRUCTIONAL MATERIALS:

  • Protractor
  • Whiteboard and marker
  • Angle charts
  • Worksheets

 

PERIOD 1 & 2: Sum of Angles on a Straight Line

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Explains the concept of angles on a straight line, demonstrating with visuals.

Pupils listen, ask questions, and observe visuals.

Step 2 - Explanation

Demonstrates that angles on a straight line add up to 180°.

Pupils repeat and practice.

Step 3 - Demonstration

Draws a straight line with various angles and demonstrates the sum.

Pupils practice drawing lines and measuring angles.

Step 4 - Note Taking

Teacher writes the key theorem on the board.

Pupils copy the theorem and examples.

NOTE ON BOARD:

  • Sum of angles on a straight line = 180°
  • Example: 50° + 130° = 180°

EVALUATION (5 exercises):

  1. What is the sum of angles on a straight line?
  2. If one angle is 60°, what is the other angle on the same straight line?
  3. Prove that 75° + 105° = 180°.
  4. If two angles on a straight line are 40° and 140°, what is their sum?
  5. Solve for the missing angle if one angle is 85°.

CLASSWORK (5 tasks):

  1. Draw a straight line and measure two angles on it.
  2. Find the missing angle when one angle is 110°.
  3. Solve: 50° + ___ = 180°.
  4. Draw a line and label two angles on it.
  5. Calculate: 65° + ___ = 180°.

ASSIGNMENT (5 tasks):

  1. Draw a straight line and measure two angles on it.
  2. Find the missing angle when one angle is 25°.
  3. Prove that 135° + 45° = 180°.
  4. Solve for the missing angle if one is 95°.
  5. Solve for the missing angle when one is 105°.

 

PERIOD 3 & 4: Supplementary Angles

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces supplementary angles, explains their relationship (add up to 180°).

Pupils listen and ask questions.

Step 2 - Explanation

Demonstrates the concept of supplementary angles using examples.

Pupils observe and practice with examples.

Step 3 - Demonstration

Draws pairs of angles that are supplementary and explains the sum.

Pupils solve supplementary angle problems with guidance.

Step 4 - Note Taking

Teacher writes key facts on the board.

Pupils copy examples and notes.

NOTE ON BOARD:

  • Supplementary angles add up to 180°.
  • Example: 120° + 60° = 180°
  • If one angle is 90°, the other must also be 90° to be supplementary.

EVALUATION (5 exercises):

  1. What is the sum of two supplementary angles?
  2. If one angle is 100°, what is the other angle in the pair?
  3. Prove that 75° and 105° are supplementary angles.
  4. Find the supplementary angle of 45°.
  5. Solve for the missing angle if one angle is 160°.

CLASSWORK (5 tasks):

  1. Solve for the missing angle in a supplementary pair of 80° and ____.
  2. Find two angles that are supplementary to 130°.
  3. Prove that 85° and 95° are supplementary.
  4. Solve for the other angle in a pair of supplementary angles when one is 50°.
  5. Solve: 100° + ___ = 180°.

ASSIGNMENT (5 tasks):

  1. Solve for the missing angle if one is 45°.
  2. Draw two supplementary angles and solve for the missing one.
  3. Find the supplementary angle of 135°.
  4. Prove that 60° + 120° are supplementary angles.
  5. Solve for the missing angle if one is 80°.

 

PERIOD 5: Complementary Angles and Sum of Angles of a Triangle

PRESENTATION:

Step

Teacher’s Activity

Pupil’s Activity

Step 1 - Introduction

Introduces complementary angles (sum is 90°) and the sum of angles of a triangle (sum is 180°).

Pupils listen and ask questions.

Step 2 - Explanation

Demonstrates complementary and triangle angle sum concepts using visuals.

Pupils observe and participate in the demonstration.

Step 3 - Demonstration

Draws examples of complementary angles and triangles, solving for missing angles.

Pupils solve complementary angle and triangle problems.

Step 4 - Note Taking

Teacher writes key concepts on the board.

Pupils take notes.

NOTE ON BOARD:

  • Complementary angles add up to 90°.
  • The sum of angles in a triangle = 180°.
  • Example: 45° + 45° = 90° (Complementary)
  • Example: 60° + 60° + 60° = 180° (Triangle)

EVALUATION (5 exercises):

  1. What is the sum of complementary angles?
  2. Find the complementary angle of 30°.
  3. What is the sum of angles in a triangle?
  4. Prove that 50° + 40° = 90° (Complementary).
  5. Solve for the missing angle in a triangle where the angles are 50° and 60°.

CLASSWORK (5 tasks):

  1. Find the complementary angle of 40°.
  2. Solve for the missing angle in a triangle with angles 50° and 60°.
  3. Prove that 30° and 60° are complementary.
  4. Calculate the third angle in a triangle with angles 80° and 45°.
  5. Solve for the missing angle in a triangle where the angles are 90° and 45°.

ASSIGNMENT (5 tasks):

  1. Solve for the complementary angle if one is 70°.
  2. Draw a triangle and find the missing angle.
  3. Solve: 30° + ___ = 90° (Complementary).
  4. Solve for the third angle in a triangle where the angles are 60° and 60°.

Find the complementary angle for 85°.