The Lawyer’s Proofbook
Edition 14, Lesson 14.2: Two-Column Proofs
Part I: Identifying the Reason
For each statement, provide the correct Reason from the "Catalog of Laws" (Given, Definition of Midpoint, Substitution, etc.).
1.
Statement: "Segment AB = Segment BA"
Reason: ________________________________________________
2.
Statement: "If M is the midpoint of XY, then XM = MY"
Reason: ________________________________________________
3.
Statement: "If ∠A = ∠B and ∠B = ∠C, then ∠A = ∠C"
Reason: ________________________________________________
Part II: Fill-in-the-Blank Proofs
Complete the missing links in these chains of logic.
4.
The Segment Addition Proof:
Given: Point B sits between A and C. AB = 5, BC = 10.
Goal: Prove AC = 15.
| Statements |
Reasons |
| 1. Point B is between A and C. |
1. **Given** |
| 2. AB = 5, BC = 10 |
2. **Given** |
| 3. AB + BC = AC |
3. ________________________ |
| 4. 5 + 10 = AC |
4. ________________________ |
| 5. 15 = AC |
5. Simplification |
Part III: Building the Brief
Write a full Two-Column Proof for the following geometric truths.
5.
The Angle Proof:
Given: ∠1 and ∠2 are complementary (they add to 90°). ∠1 = 30°.
Goal: Prove ∠2 = 60°.
6.
The Transitive Path:
Given: Line AB = CD. Line CD = EF.
Goal: Prove Line AB = EF.
Part IV: Identifying the Rupture
In the following "Feral Proof," identify where the Lawyer took an unsupported step.
7.
The Feral Claim:
Step 1: Point M is between X and Y. (Given)
Step 2: XM = MY. (Reason: It looks like it is in the middle).
Step 3: M is the midpoint. (Reason: Definition of Midpoint).
Where is the Rupture? ________________________________________________
What was missing? ________________________________________________
Part V: Kingdom Modeling
8.
The Proof of the Vow:
Given: You have made a vow to the King ($p$). The King honors those who keep their word ($q$).
Goal: Prove that your faithfulness leads to the King's honor.
| Statements |
Reasons |
| 1. I have made a vow to the King. |
1. ________________________ |
| 2. If I keep my vow, then the King honors me. |
2. Given (Covenant Law) |
| 3. I keep my vow. |
3. Definition of Integrity. |
| 4. The King honors my faithfulness. |
4. **Modus Ponens** (Lesson 14.1) |
Part VI: The Echad Extension (Transmission)
9.
The "Why" Game:
Sit with a younger child. Ask them to make a claim (e.g., "I am hungry" or "The sky is blue"). Then, ask them "Why?" for every reason they give, until you reach a fundamental "Given" (e.g., "Because God made it that way" or "Because my stomach is growling"). Record the chain of reasons below. How did you explain that every step needs a support?
Part VII: Logic and Reflection
10.
The Rupture of the Jump:
A student writes a proof where Step 2 is the Given, and Step 3 is the Goal. They say the reason is "Common Sense." Why is this a failure of the Lawyer's duty? How does it leave the "Building" vulnerable?
11.
The Stability of the Word:
Explain how the "Reasons" column in geometry is like the "Scripture" in a Christian argument. Why can't we just make claims on the left side of our life without having an authority on the right? How does this protect the "Glass Box" of our character?
12.
The Law of Identity:
Why is the **Reflexive Property** ($a = a$) necessary in a proof? Even though it seems obvious, how does stating it protect the chain from a "Missing Link" rupture?
"I vow to show my reasons. I will not walk in the shadow of 'maybe', but in the light of the proven Word. I will be a faithful Lawyer for the King, building my life stone by stone on the foundation of the Truth. My precision shall be my witness."
[VOLUME 2 WORKBOOK SPEC: 14.2]
This workbook introduces the formal structure of the two-column proof. It reinforces the use of properties of equality and basic geometric definitions as reasons.
Total Practice Items: 8
Theological Anchor: Accountability/Justification