A triangle has angles 62° and 68°. Find the third angle.
Unit 03 · Lesson 06 · Triangle Congruence & Proof
Triangle Inequality & Feasible Construction
Test feasible side lengths and determine the range of a missing side before attempting construction.
Learning intention
Use accurate diagrams, definitions, measurements, and reasoning to test feasible side lengths and determine the range of a missing side before attempting construction.
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
Triangle Inequality & Feasible Construction
Find, construct, prove, or explain each result. Show reasoning and label units.
Name
Date
Two sides are 7 and 8. State the integer range for the third side x.
Which congruence theorem uses two sides and the included angle?
After proving ΔABC≅ΔDEF, which angle corresponds to ∠B?
Where do the perpendicular bisectors of a triangle meet?
Why does AAA not prove triangle congruence?