Students will be able to apply the Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) triangle congruence shortcuts to determine if two triangles are congruent.
Students will be given a set of triangles and will need to determine if the given information proves the two triangles congruent using either ASA or AAS.
Angle-Side-Angle (ASA) Congruence Postulate: If two angles and the included side in one triangle are congruent to two angles and the included side in another triangle, then the two triangles are congruent.
Formula: If ∠A ≅ ∠X, ∠B ≅ ∠Y, and AB ≅ XY, then △ABC ≅ △XYZ.
Angle-Angle-Side (AAS) Congruence Theorem: If two angles and a non-included side in one triangle are congruent to two angles and the corresponding non-included side in another triangle, then the triangles are congruent.
Formula: If ∠A ≅ ∠X, ∠B ≅ ∠Y, and BC ≅ YZ, then △ABC ≅ △XYZ.
Understand the Angle-Side-Angle (ASA) Congruence Postulate and the Angle-Angle-Side (AAS) Congruence Theorem
Identify when the given information in two triangles satisfies the conditions for ASA or AAS congruence
Apply the congruence shortcuts to verify if two triangles are congruent
Differentiate between ASA and AAS criteria for triangle congruence
Review what students know about triangle congruence
Present a scenario where two friends are trying to prove if two triangles are congruent and ask students to predict how they will do it
Explain the definitions of ASA and AAS congruence shortcuts
Provide examples illustrating the criteria for ASA and AAS congruence
Misconception: Emphasize that the order of the angles and sides must match in both triangles for congruence
Show examples of triangles and guide students through determining congruence with ASA and AAS
Scaffold questioning from simpler cases to more complex scenarios
Monitor student performance by walking around the class and providing immediate feedback
Students will work on a worksheet where they need to determine if the given triangles are congruent using ASA or AAS
Encourage students to explain their reasoning for each congruence using the correct terminology
Have students share their findings with a partner and summarize the key differences between ASA and AAS congruence
Review the main points of the lesson as a whole class
Challenge early finishers to create their own pair of congruent triangles using either ASA or AAS
Assign students to find real-life examples where ASA or AAS congruence can be applied to prove triangles congruent
CCSS.MATH.CONTENT.HSG.CO.D.14a: Prove theorems about triangles
CCSS.MATH.CONTENT.HSG.CO.D.14b: Make geometric constructions