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coordinate-proof

Proves geometric theorems using distance, midpoint, and slope formulas on coordinate systems.

3|Updated Feb 9, 2026
Search Tags:#geometry#lean#proof#distance#coordinate#analytic#slope
One-click install
npx skills add https://github.com/0bserver07/bourbaki --skill coordinate-proof
Or copy as Structured Prompt for Agent▼
Please help me install this Agent Skill.
Skill: coordinate-proof
Source: https://github.com/0bserver07/bourbaki/tree/main/src/skills/coordinate-proof
Command: npx skills add https://github.com/0bserver07/bourbaki --skill coordinate-proof

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Prove geometric statements by placing figures in a coordinate system and using algebraic computations.

Core Features & Use Cases

  • Prove geometric relationships in a coordinate plane using distance, midpoint, and slope formulas.
  • Convert geometric configurations into algebraic equations and verify properties like parallelism, perpendicularity, and diagonal bisection.
  • Provide optional Lean formalization for machine-checked proofs when needed.

Quick Start

Place a figure in coordinates and derive the theorem using distance, midpoint, and slope formulas.

Frequently Asked Questions about coordinate-proof

High-intent search queries and answers about installing and using this skill.

FAQPage Schema
How do I prove geometric theorems using coordinate algebra?▼

Proving geometric theorems with coordinate algebra involves placing figures like triangles and rectangles in a coordinate plane, then using distance, midpoint, and slope formulas to verify properties such as parallelism and perpendicularity.

What is the coordinate proof method for verifying geometric properties?▼

The coordinate proof method converts geometric configurations into algebraic equations. By applying distance, midpoint, and slope formulas, you can verify properties like parallelism, perpendicularity, and diagonal bisection for figures in a coordinate plane.

How do I use slope and distance formulas to prove properties of triangles and rectangles?▼

You can use slope and distance formulas to prove properties of triangles and rectangles by placing them in a coordinate plane and converting their geometric configurations into algebraic equations to verify characteristics like parallelism and diagonal bisection.

Can I use Lean formalization for machine-checked coordinate proofs?▼

Yes, you can use optional Lean formalization to support machine-checked coordinate proofs. This allows you to verify the algebraic derivations of distance, midpoint, and slope formulas with formal logic.

Do I need to place figures in a coordinate system to verify perpendicularity and parallelism?▼

Yes, placing figures in a coordinate system is required to verify perpendicularity and parallelism. This placement allows you to convert geometric configurations into algebraic equations using slope and distance formulas for the proof.

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