CK-12 Geometry Concepts

http://www.ck12.org Chapter 2. Reasoning and Proof

TABLE2.23:(continued)

Statement Reason

3.^6 1 and^6 2 are supplementary

(^6) 2 and (^6) 3 are supplementary

3. Linear Pair Postulate

4.m^61 +m^62 = 180 ◦

m^62 +m^63 = 180 ◦

4. Definition of Supplementary Angles

5.m^61 +m^62 =m^62 +m^63 5. SubstitutionPoE

6.m^61 =m^63 6. SubtractionPoE

7.^61 ∼=^63 7.∼=angles have = measures

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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
5.^62 ∼=^63 5. SubtractionPoE

2.