Cogito
Geometry · Chapter 3 · Lesson 2
Writing a Two-Column Proof
Every claim carries its reason.
11 problems · about 24 minutes · G-CO.C.9, G-CO.B.8
What this lesson teaches
The student writes a short two-column proof with justified steps.
- A two-column proof pairs every statement with a reason.
- The given information opens the proof and needs no justification.
- Only definitions, postulates, and proved theorems count as reasons.
Warm Up
Straightforward practice. Get the method working first.
4 problemsIs "given" a valid reason for a first line? 1 for yes, 0 for no.
Answer 1
Why Yes.
Order the lines of a two-column proof.
Answer 1. State the given information 2. Derive intermediate facts with reasons 3. Name the criterion being applied 4. State the conclusion
Why The given never needs proving.
How many columns does a two-column proof have?
Answer 2
Why Statements and reasons.
Is a definition a valid reason? 1 for yes, 0 for no.
Answer 1
Why Definitions are agreed.
Build It Up
The same ideas with more to keep track of.
3 problemsIs an unproved conjecture a valid reason? 1 for yes, 0 for no.
Answer 0
Why It must already be established.
Select every acceptable reason in a proof.
Answer A definition; A postulate; A theorem already proved
Why Three of the four are established facts.
Does the reflexive property let a shared side equal itself? 1 for yes, 0 for no.
Answer 1
Why Anything equals itself.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsA proof concludes something not asked for. Is it complete? 1 for yes, 0 for no.
Answer 0
Why It must reach the stated goal.
How many pairs must match for SSS?
Answer 3
Why Three sides.
The Criterion: Two sides and the included angle. How many pairs are used? Give the count of matched pairs.
Answer 3
Why 3.
The Reason: Is "the diagram looks that way" a valid reason? 1 for yes, 0 for no.
Answer 0
Why No.