Proof in Three Voices: Flow, Paragraph, and Two-Column Proofs
Shared by A STEM Educator
Students will be able to construct and translate geometric proofs (flow, paragraph, and two-column format) involving angle relationships, congruence, and triangle properties, progressing from 4-step guided proofs to 10-step independent proofs.
Lesson Overview
Students progress from completing a 4-step proof scaffold to constructing an independent 10-step proof, translating the same logical argument across all three proof formats. Each task changes exactly one variable — proof length, format, or complexity of the geometric relationship.
Materials
- Vertical whiteboards or chart paper
- Dry-erase markers (multiple colors)
- Random grouping tool
- Printed given/diagram reference cards
- Rulers and protractors for reference
Scaffolded Task Progression
Given: ∠1 and ∠2 are supplementary; m∠1 = 110°
Prove: m∠2 = 70°
[ Interactive graph / diagram — available in the full lesson ]
Flow Proof (fill in the blanks):
[∠1 and ∠2 are supplementary] → [m∠1 + m∠2 = 180°] → [110° + m∠2 = 180°] → [m∠2 = 70°]
Given ___?___ ___?___ ___?___
Given: ∠1 and ∠2 are supplementary; m∠1 = 110°
Prove: m∠2 = 70°
This is the SAME proof as Task 1 — now write it in two-column format.
| Statements | Reasons |
|---|---|
| 1. ∠1 and ∠2 are supplementary | 1. ___?___ |
| 2. m∠1 + m∠2 = 180° | 2. ___?___ |
| 3. 110° + m∠2 = 180° | 3. ___?___ |
| 4. m∠2 = 70° | 4. ___?___ |
Given: ∠1 and ∠2 are supplementary; m∠1 = 110°
Prove: m∠2 = 70°
Write 3-4 complete sentences that prove m∠2 = 70°. Every claim must include its justification.
Sentence starter: 'Since ∠1 and ∠2 are supplementary, we know that...'
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