Prove Statements about Segments and Angles

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Presentation transcript:

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: Prove: 2 Column Proof: A C B D 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: A C B D Statement Reason ABD is a right angle Given m ABD = 90˚ Def. Right Angle Point C is in the interior of ABD m ABD = m ABC + m CBD Angle Add. Postulate 90˚= m ABC + m CBD Substitution ABC and CBD are complementary Definition of complementary angles

Practice B