🔷 Geometry — Congruence
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Two-Column Proofs

Write formal geometric proofs using statements and justified reasons.

A two-column proof has statements in the left column and reasons in the right column. Each statement must follow logically from previous statements, using definitions, postulates, or theorems as justification.

Structure of a Two-Column Proof

Given: state what information is providedProve: state what you need to showColumn 1 (Statements): logical steps toward the goalColumn 2 (Reasons): definition, postulate, or theorem name
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Common reasons: Given, Definition of midpoint/bisector, Reflexive Property (a = a), Transitive Property, SAS/ASA/SSS/AAS/HL, CPCTC.

📐Two-Column Proof Example
Given: M is the midpoint of AB and CD. Prove: △AMC ≅ △BMD.
1. M is the midpoint of AB | Given
2. AM = MB | Definition of midpoint
3. M is the midpoint of CD | Given
4. CM = MD | Definition of midpoint
5. ∠AMC = ∠BMD | Vertical Angles Theorem
6. △AMC ≅ △BMD | SAS
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Remember This!

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) can only be used AFTER you have already proven the triangles congruent — it is a consequence, not a starting reason.

✏️ Try It!

In a two-column proof, you state "AB = AB." What reason justifies this statement?

Take Quiz 📝 — 25 Questions