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Cogito

Geometry · Chapter 3 · Lesson 2

Practice Worksheet

Writing a Two-Column Proof

Every claim carries its reason.

11 problems · about 24 minutes · G-CO.C.9, G-CO.B.8

NameDate

Figure — use these to answer the problems

The figure a proof argues about. Turning it changes nothing that matters.

Triangle

Straight sides

3

Corners

3

Turn it0
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. Is "given" a valid reason for a first line? 1 for yes, 0 for no.

    Answer

  2. Order the lines of a two-column proof.

    Write 1 to 4 in the boxes to put these in order.

    • State the given information
    • Derive intermediate facts with reasons
    • Name the criterion being applied
    • State the conclusion

  3. How many columns does a two-column proof have?

    Answer

  4. Is a definition a valid reason? 1 for yes, 0 for no.

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Is an unproved conjecture a valid reason? 1 for yes, 0 for no.

    Answer

  2. Select every acceptable reason in a proof.

    • A definition
    • A postulate
    • The diagram appears that way
    • A theorem already proved
    • Tick every box that applies.

  3. Does the reflexive property let a shared side equal itself? 1 for yes, 0 for no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. A proof concludes something not asked for. Is it complete? 1 for yes, 0 for no.

    Answer

  2. How many pairs must match for SSS?

    Answer

  3. The Criterion

    Two sides and the included angle. How many pairs are used? Give the count of matched pairs.

    Answer

  4. The Reason

    Is "the diagram looks that way" a valid reason? 1 for yes, 0 for no.

    Answer