prove statements about segments and angles section 2.6

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.

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

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.

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

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

Practice B