synthetic-construction

Prove geometric theorems using compass-and-straightedge constructions and congruence criteria.

3|Updated Feb 9, 2026

Search Tags:#geometry #similarity #construction #proof #synthetic #congruence

Ready to run

npx skills add https://github.com/0bserver07/bourbaki --skill synthetic-construction

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: synthetic-construction
Source: https://github.com/0bserver07/bourbaki/tree/main/src/skills/synthetic-construction
Command: npx skills add https://github.com/0bserver07/bourbaki --skill synthetic-construction

SYSTEM DOCUMENTATION & REQUIREMENTS

What problem does it solve?

Prove geometric theorems using classical compass-and-straightedge reasoning by guiding users through structured auxiliary constructions and rigorous congruence and similarity arguments.

Core Features & Use Cases

Auxiliary constructions reveal hidden structure and transform difficult problems into solvable ones.
Apply standard triangle congruence criteria (SSS, SAS, ASA, AAS) and similarity criteria (AA, SAS~, SSS~) with clear justification and CPCTC.
Triggers on natural prompts like "prove congruent", "prove similar", "construct" to initiate a complete synthetic geometry proof workflow.

Quick Start

Construct the necessary auxiliary lines and then apply the standard congruence and similarity rules to complete the proof.

Frequently Asked Questions about synthetic-construction

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

FAQPage Schema

How do I prove triangle congruence using SSS, SAS, ASA, and AAS criteria step by step?▼

Prove triangle congruence by constructing auxiliary lines and applying SSS, SAS, ASA, or AAS criteria with CPCTC justifications. The workflow guides each synthetic geometry inference with clear citations and step-by-step construction logic.

What is synthetic geometry and how does compass-and-straightedge construction work for proofs?▼

Synthetic geometry proves theorems through classical compass-and-straightedge construction without coordinate algebra. It reveals hidden structural relationships by building auxiliary figures, enabling rigorous congruence and similarity arguments across Euclidean geometry.

How do I use auxiliary constructions to prove similarity in Euclidean geometry problems?▼

Use auxiliary constructions to expose hidden proportional relationships, then apply AA, SAS~, or SSS~ similarity criteria. The process transforms difficult Euclidean geometry problems into structured, solvable similarity arguments with clear step-by-step justifications.

Can I use CPCTC conclusions after applying standard congruence criteria in a geometry proof?▼

Apply CPCTC conclusions directly after establishing triangle congruence via SSS, SAS, ASA, or AAS. The synthetic construction workflow supports CPCTC-style inferences with explicit citations for each corresponding part conclusion.

What is the best way to structure a step-by-step geometric proof with justifications for each inference?▼

Structure your geometric proof by first constructing necessary auxiliary lines, then applying congruence or similarity rules sequentially. Each inference requires clear citations, ensuring rigorous justification from construction through CPCTC conclusions.

Are there limitations to synthetic geometry proofs when dealing with complex algebraic relationships?▼

Synthetic geometry proofs focus on compass-and-straightedge reasoning and may not handle complex algebraic coordinate relationships. For problems requiring analytic geometry calculations, consider alternative approaches outside classical construction-based methods.