M2L5 Congruence - Investigating (Part 1)

M2L5 Congruence - Integrated Mathematics 9

Lesson Overview

• Today's question: Define "congruent" in your own words. Example required using angles or shapes.

• Objectives for today:

  • Prior Learning: Review previous knowledge on congruence.

  • Investigating Triangle Congruence: Understand congruence in triangles.

  • Checking Understanding: Confirm comprehension of the topic.

Congruent Figures

• Definition: Two shapes are congruent when they are:

  • Identical in size and shape.

  • They do not need to have the same position or orientation.

• Important: When two figures are congruent:

  • Write corresponding vertices in the same order.

  • Use the symbol ≅ to indicate congruence (e.g., ABCD ≅ PQRS).

Naming Polygons

• To name a polygon, use the consecutive order of vertices.

  • Example: Polygon PQRS can be named as QRSP or SRQP but NOT PRQS.

• In a congruence statement, the order signifies the corresponding parts:

  • E.g., ΔABC ≅ ΔDEF conveys which parts correspond.

Investigating Triangle Congruence

Steps for Investigation

1. In teams, discover what makes two triangles congruent.

2. Identify the necessary information to confirm congruence.

• Key criteria may include side lengths and angle measures.

Triangle Construction Exercise

• Teams will receive sets of specific criteria to build triangles:

  • Use rulers, protractors, and materials provided to draw/build triangles.

  • Teacher approval required after construction.

Criteria for Triangle Congruence

Sufficient Conditions

• SSS (Side-Side-Side): All three pairs of sides are congruent.

• SAS (Side-Angle-Side): Two sides and the included angle must be congruent.

• ASA (Angle-Side-Angle): Two angles and the included side must be congruent.

• AAS (Angle-Angle-Side): Two angles and one side opposite them must be congruent.

• HL (Hypotenuse-Leg): For right triangles, the hypotenuse and one leg must be congruent.

Insufficient Conditions

• SSA (Side-Side-Angle): Two sides and a non-included angle do NOT guarantee congruence (can yield different triangles).

• AAA (Angle-Angle-Angle): Three angles being congruent does NOT imply that the triangles are congruent; they may vary in size.

Conclusion and Reflection

• Reflection on the triangle congruence criteria.

• Discuss criteria for Building Project 5 to ensure congruent triangles.

Additional Tasks

• If time allows, create a set of notes with diagrams to reinforce learning. Teachers are available to assist with this task!