PROVE STATEMENTS ABOUT SEGMENTS AND ANGLES Section 2.6.
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Transcript of PROVE STATEMENTS ABOUT SEGMENTS AND ANGLES Section 2.6.
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PROVE STATEMENTS ABOUT SEGMENTS AND ANGLES
Section 2.6
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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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Practice B