Exploring Triangle Congruence with HL Theorem

Objective:

Students will be able to apply the Hypotenuse-Leg (HL) Congruence Theorem to determine if two right triangles are congruent.

Assessment:

Students will be assessed on their ability to identify congruent right triangles using the HL Congruence Theorem through a worksheet containing various triangle pairs for comparison.

Key Points:

• Hypotenuse-Leg (HL) Congruence Theorem: If the hypotenuse and leg in one right triangle are congruent to the hypotenuse and leg in another right triangle, then the two triangles are congruent.
  Formula: If in right triangles ABC and DEF, AB = DE and AC = DF, then triangle ABC is congruent to triangle DEF by the HL Congruence Theorem.

• Understand the Hypotenuse-Leg (HL) Congruence Theorem

• Identify criteria for triangle congruence

• Apply the HL Congruence Theorem to determine triangle congruence

Opening:

• Introduce the concept of triangle congruence using a real-life scenario or visual aid

• Ask students to discuss with a partner why they think certain triangles look congruent

Introduction to New Material:

• Explain the HL Congruence Theorem and its significance in determining triangle congruence

• Provide examples of congruent right triangles using the HL criteria

• Anticipate misconception: Assuming all triangles with equal sides are congruent

Guided Practice:

• Engage students in identifying matching sides and angles in pairs of triangles

• Progress from simple to complex examples for students to practice applying the HL Congruence Theorem

• Monitor student progress by circulating the classroom and providing guidance as needed

Independent Practice:

• Assign a worksheet with various sets of right triangles for students to determine congruence using the HL Theorem

• Encourage students to justify their answers with explanations and diagrams

• Monitor independent work time and provide support where necessary

Closing:

• Have students share their findings with the class on which triangles they identified as congruent and how they applied the HL Theorem

• Summarize the key points of the lesson and clarify any lingering questions

Extension Activity:

• Create a challenge where students need to prove the congruence of triangles using a combination of the HL Theorem and other congruence criteria

Homework:

• Homework suggestion: Ask students to find examples in everyday life where the HL Congruence Theorem could be applicable and explain their reasoning.

Standards Addressed:

• CCSS.MATH.CONTENT.HSG.CO.D.15: Prove theorems about triangles

• CCSS.MATH.CONTENT.HSG.CO.D.15a: Give informal arguments for the formulas of the area of a triangle using perpendicular sides and the angle between them