The Book of Precedents
Edition 14, Lesson 14.3: Established Laws
Part I: Postulate or Theorem?
For each statement, determine if it is a **Postulate** (accepted without proof) or a **Theorem** (requires proof).
1.
"If two angles are vertical angles, then they are equal."
Type: ________________________
2.
"A line contains at least two points."
Type: ________________________
3.
"All right angles are equal to each other."
Type: ________________________
Part II: Efficient Proofs (Using Theorems)
Use established Theorems to complete these proofs with minimum steps.
4.
Given: Diagram shows ∠1 and ∠3 are vertical angles.
Goal: Prove ∠1 ≅ ∠3.
| Statements |
Reasons |
| 1. ∠1 and ∠3 are vertical angles. |
1. ________________________ |
| 2. ∠1 ≅ ∠3 |
2. ________________________ |
5.
The Right Angle Witness:
Given: ∠A is a right angle. ∠B is a right angle.
Goal: Prove ∠A ≅ ∠B.
| Statements |
Reasons |
| 1. ∠A is a right angle. ∠B is a right angle. |
1. **Given** |
| 2. ∠A ≅ ∠B |
2. ________________________ |
6.
The Complementary Witness:
Given: ∠1 is complementary to ∠2. ∠3 is complementary to ∠2.
Goal: Prove ∠1 ≅ ∠3.
(Reason: Use the **Congruent Complements Theorem**)
| Statements |
Reasons |
| 1. ∠1 is comp. to ∠2. ∠3 is comp. to ∠2. |
1. **Given** |
| 2. ∠1 ≅ ∠3 |
2. ________________________ |
Part III: Symbolic Shorthand (The Language of the Hall)
Translate these "Feral Sentences" into the "Lawyer's Shorthand" using symbols (≅, ⊥, ∠, ||).
6.
"Angle 1 is congruent to angle 2."
Shorthand: ________________
7.
"Line AB is perpendicular to line CD."
Shorthand: ________________
8.
"Angle PQR has a measure of 90 degrees."
Shorthand: ________________
Part IV: The Congruent Supplements Challenge
9.
Given: ∠1 is supplementary to ∠2. ∠3 is supplementary to ∠2.
Goal: Prove ∠1 ≅ ∠3.
| Statements |
Reasons |
| 1. ∠1 is supp. to ∠2. ∠3 is supp. to ∠2. |
1. **Given** |
| 2. ∠1 ≅ ∠3 |
2. ________________________ |
10.
The Reflexive Anchor:
Why is Step 2 necessary in this proof?
Step 1: Segment AB is a shared side. (Given)
Step 2: AB ≅ AB. (Reason: ________________)
Your Reflection: ________________________________________________
Part V: Kingdom Modeling
11.
The Doctrine of the Creed:
In your own words, explain how a "Creed" (like the Apostles' Creed) is like a "Theorem" in the Library of Precedents. Why is it helpful to have these summaries of truth already established? How does this protect the "Glass Box" of the Church's teaching?
12.
The Consistency of the King:
If God's laws were like "Postulates" that changed every day (e.g., if He decided today that stealing was good), could we build a "Theorem" for our lives? Why is the permanence of mathematical laws a reflection of God's unchanging nature (Immutability)?
Part VI: The Echad Extension (Transmission)
13.
The Heritage Challenge:
Ask an older family member or a mentor for a "Family Theorem"—a lesson they have proven to be true through their life experience. Write it as an **If/Then** statement. Explain to them that their life experience has moved this truth from a "Statement" to a "Reason" for the next generation. Record their reaction below.
Part VII: Logic and Final Audit
14.
The Chain of Witnesses:
Why is it better to cite a single Theorem than to repeat a 5-step proof every time? How does this "Efficiency of Truth" help the Lawyer handle more complex cases in the future?
"I vow to build my house on the rock of established truth. I will respect the labor of those who walked the Hall before me, and I will be a faithful steward of the Library of Precedents. My logic shall be my legacy."
[VOLUME 2 WORKBOOK SPEC: 14.3]
This workbook focuses on the transition from basic postulates to derived theorems. It reinforces the efficiency of using established laws as reasons in formal proofs.
Total Practice Items: 8
Theological Anchor: Tradition/Stability