A triangle has angles 37° and 50°. Find the third angle.
Answer: 93
Reasoning: Triangle angles sum to 180°.
Reasoning: Triangle angles sum to 180°.
Unit 03 · Lesson 03 · Triangle Congruence & Proof
ASA, AAS and HL Congruence · Teacher Key
Identify sufficient evidence for triangle congruence and organize theorem-based proofs about corresponding parts and centers.
Learning intention
Use accurate diagrams, definitions, measurements, and reasoning to identify sufficient evidence for triangle congruence and organize theorem-based proofs about corresponding parts and centers.
Success evidence
- Label the figure and units before calculating.
- Select and justify the governing definition, theorem, relationship, or construction.
- Show enough work that another learner can audit the conclusion.
- Check the result against the diagram, scale, and stated constraints.
Visual model
Identify sufficient evidence for triangle congruence and organize theorem-based proofs about corresponding parts and centers.
m\angle A+m\angle B+m\angle C=180^\circa+b>cSSS,\ SAS,\ ASA,\ AAS,\ HL
Worked reasoning
Process: Match vertices in a consistent correspondence, mark the known evidence, select the valid congruence theorem, then use CPCTC only after congruence is established.
- Read the figure and rewrite all given information with correct notation.
- Identify the exact relationship that connects the known and unknown quantities.
- Substitute, construct, or prove one justified step at a time.
- State the result with units and a sentence explaining what it means.
Misconception check: AAA proves similarity, not congruence; SSA is not a general congruence theorem.
Khaemenes Academy · Open-Age Geometry
ASA, AAS and HL Congruence
Find, construct, prove, or explain each result. Show reasoning and label units.
Name
Date
Two sides are 5 and 7. State the integer range for the third side x.
Answer: 2<x<12
Reasoning: Use the triangle inequality and the difference inequality.
Reasoning: Use the triangle inequality and the difference inequality.
Which congruence theorem uses two sides and the included angle?
Answer: SAS
Reasoning: The angle must be between the two known sides.
Reasoning: The angle must be between the two known sides.
After proving ΔABC≅ΔDEF, which angle corresponds to ∠B?
Answer: ∠E
Reasoning: The order of vertices determines correspondence.
Reasoning: The order of vertices determines correspondence.
Where do the perpendicular bisectors of a triangle meet?
Answer: Circumcenter
Reasoning: It is equidistant from all three vertices.
Reasoning: It is equidistant from all three vertices.
Why does AAA not prove triangle congruence?
Answer: It fixes shape but not size
Reasoning: AAA establishes similarity.
Reasoning: AAA establishes similarity.