Geometry / Unit 2: Reasoning and Proof
2.5 Two-Column Proofs
Notes
A proof is a logical argument. A two-column proof lists statements on the left and reasons on the right.
- Start with the given information. End with what you want to prove.
- Reasons can be: given, definitions, postulates, properties, or theorems already proved.
- Example: Given $2x + 5 = 17$. Prove $x = 6$.
- $2x + 5 = 17$ (Given); $2x = 12$ (Subtraction Prop.); $x = 6$ (Division Prop.).
Practice
In a proof, the statement $M$ is the midpoint of $\overline{AB}$ is followed by $\overline{AM} \cong \overline{MB}$. What is the reason?
A midpoint, by definition, splits a segment into two congruent segments.
Given: $\displaystyle \frac{x}{4} - 1 = 2$. After $\displaystyle \frac{x}{4} = 3$, the next step $x = 12$ uses which property?
Both sides are multiplied by 4.
What should the first line of most two-column proofs contain?
Proofs start from what is given and work toward what is to be proved.
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