prove statements about segments and angles section 2.6

PROVE STATEMENTS ABOUT SEGMENTS AND ANGLES Section 2.6

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PROVE STATEMENTS ABOUT SEGMENTS AND ANGLES

Section 2.6

Proofs

Proofs are logical arguments that explains why a statement is true.

Proofs use theorems, postulates, formulas, and definitions to prove facts to be true.

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Theorems

Theorems are statements that can be proven true.

There are many theorems that have already been proven true that we can use in order to prove different statements

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2 column proofs

Most of the proofs that we will do in this class will be 2 column proofs

2 column proofs have the steps towards proving a statement in the first column and the reasons (postulates, definitions, theorems, and formulas) in the second column.

We did algebraic 2 column proofs in the last section.

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Algebraic Proof

Prove that x = 9 when given 2(x – 7) = 4x – 32

2(x – 7) = 4x – 32 Given 2x – 14 = 4x – 32 Distribution Property -14 = 2x – 32 Subtraction Property 18 = 2x Addition Property 9 = x Division Property

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Geometric Proof Given:

Point C is in the interior of Angle ABD. Angle ABD is a right angle.

Prove: Angle ABC and Angle CBD are complementary.

2 Column Proof:

Statement Reason

ABD is a right angle Given

m ABD = 90˚ Def. Right Angle

Point C is in the interior of ABD

Given

m ABD = m ABC + m CBD

Angle Add. Postulate

90˚= m ABC + m CBD Substitution

ABC and CBD are complementary

Definition of complementar

y angles

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