CK-12 Geometry-Concepts

2.8. Two-Column Proofs http://www.ck12.org

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CK-12 Foundation: Chapter2TwoColumnProofsB

Vocabulary

Atwo-column proofis one common way to organize a proof in geometry. Two-column proofs always have two
columns: statements and reasons.

Guided Practice

1. Write a two-column proof for the following:

Given:AC⊥BDand^61 ∼=^64

Prove:^62 ∼=^63

2. Write a two-column proof for the following:

Given:^6 Lis supplementary to^6 M,^6 Pis supplementary to^6 O,^6 L∼=^6 O

Prove:^6 P∼=^6 M

Answers:

TABLE2.24:

Statement Reason

1.AC⊥BD 1. Given

2.^6 BCAand^6 DCAare right angles 2. Definition of a Perpendicular Lines
3.^6 BCA∼=^6 DCA 3. Right Angle Theorem
4.^61 ∼=^64 4. Given
120 5.^62 ∼=^63 5. SubtractionPoE