Mathematics - Senior Secondary 1 - Deductive proofs (III)

Deductive proofs (III)

Get it on Google Play
Get it on the Apple App Store
  1. Home
  2. Comprehensive Lesson Plan and Notes
  3. Senior Secondary 1
  4. Deductive proofs (III)

Term: 3rd Term

Week: 3
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Deductive Proofs (III)

SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Identify and demonstrate properties of parallelograms and related quadrilaterals using deductive proofs.
  2. Understand and apply the Intercept Theorem.
  3. Prove that parallelograms on the same base and between the same parallel lines are equal in area.
  4. Apply paper cutouts and models in demonstrating geometric proofs.
  5. Solve geometric problems using deductive reasoning.

INSTRUCTIONAL TECHNIQUES:
• Question and answer
• Guided demonstration
• Practice exercises
• Group discussion
• Use of physical models and paper folding

INSTRUCTIONAL MATERIALS:
• Whiteboard and markers
• Chart papers and paper cutouts
• Rulers, protractors, and compasses
• Models of parallelograms and triangles
• Worksheets for practice
• Cardboard plane shapes

 

PERIOD 1 & 2: Introduction to Properties of Parallelograms and Related Quadrilaterals

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Revises basic properties of parallelograms. Introduces related quadrilaterals like rectangles, rhombuses, and squares.

Students listen and recall prior knowledge.

Step 2 - Demonstration

Uses paper cutouts and models to show: opposite sides are equal and parallel; opposite angles are equal; diagonals bisect each other.

Students observe and interact with the models.

Step 3 - Application

Leads class in proving one property deductively using geometric reasoning and prior knowledge of axioms.

Students participate in solving the proof with the teacher.

Step 4 - Group Activity

Assigns small groups to work with paper cutouts to demonstrate other properties.

Students work in groups to apply and verify properties practically.

Step 5 - Recap

Summarizes key properties on the board.

Students take notes.

NOTE ON BOARD:
• Opposite sides of a parallelogram are equal and parallel.
• Opposite angles are equal.
• Diagonals bisect each other.
• Adjacent angles are supplementary.

 

EVALUATION (5 exercises):

  1. State any three properties of a parallelogram.
  2. What is the relationship between opposite sides in a parallelogram?
  3. Prove that diagonals of a parallelogram bisect each other.
  4. Identify which quadrilateral has all sides equal and all angles equal.
  5. What type of quadrilateral has one pair of equal and parallel sides?

CLASSWORK (5 questions):

  1. Draw and label a parallelogram ABCD.
  2. Show that opposite sides of a parallelogram are equal.
  3. Prove that the diagonals of a rectangle are equal.
  4. Construct a rhombus using compass and ruler.
  5. Identify the quadrilateral whose diagonals are perpendicular bisectors of each other.

ASSIGNMENT (5 tasks):

  1. Research real-life examples of parallelograms (e.g., tiles, bridges).
  2. Illustrate a parallelogram and prove that opposite angles are equal.
  3. Draw a rectangle and show how its diagonals are equal and bisect each other.
  4. Write a short explanation of how you can identify a parallelogram.
  5. Cut a paper parallelogram and fold to prove angle and side properties.

 

PERIOD 3 & 4: Intercept Theorem and Parallelograms on Same Base

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the Intercept Theorem using diagrams and real-life examples.

Students listen and ask questions.

Step 2 - Explanation

Explains and demonstrates: If a line cuts two sides of a triangle proportionally, it is parallel to the third side.

Students follow with rulers and graphs.

Step 3 - Practice

Guides students to draw triangles and apply the intercept theorem.

Students construct and verify the theorem practically.

Step 4 - Area of Parallelograms

Explains and proves that parallelograms on the same base and between the same parallels are equal in area.

Students construct examples and compare areas.

Step 5 - Group Proof

Divides class into groups to prove the statement using cutouts.

Students collaborate and present findings.

NOTE ON BOARD:
• Intercept Theorem: If a line divides two sides of a triangle in the same ratio, it is parallel to the third side.
• Parallelograms on the same base and between same parallels are equal in area.

 

EVALUATION (5 exercises):

  1. State the Intercept Theorem.
  2. Prove that two parallelograms on the same base and between the same parallels are equal in area.
  3. Use a diagram to explain the Intercept Theorem.
  4. What must be true for two parallelograms to have equal areas?
  5. Identify one real-life application of the Intercept Theorem.

CLASSWORK (5 questions):

  1. Construct two parallelograms on the same base and between the same parallel lines.
  2. Use geometric tools to verify the Intercept Theorem.
  3. Prove the area property using paper models.
  4. State one difference between a parallelogram and a trapezium.
  5. Illustrate how the Intercept Theorem can be applied in a triangle.

ASSIGNMENT (5 tasks):

  1. Find a real-world object shaped like a parallelogram and describe it.
  2. Draw two parallelograms on the same base and parallel lines and verify their areas.
  3. Use a model to show and explain the Intercept Theorem.
  4. Research how architects use the properties of parallelograms.
  5. Write a paragraph summarizing the Intercept Theorem and area property.

 

PERIOD 5: Conclusion and Review

PRESENTATION:
• Reviews all concepts: properties of parallelograms, Intercept Theorem, area properties.
• Asks students to solve example problems on the board.
• Opens the floor for clarification and questions.
• Reinforces key takeaways through a mini quiz or recap game.

 

EVALUATION:

  1. Oral questions to assess retention.
  2. Review of classwork and assignments.

Feedback on practical model construction and reasoning.