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Unit 3 Section 3

Unit 3 Section 3. Logic: Intro to Proofs. If we want to prove a conditional statement is true, we start with the __________ and step-by-step, we show that the ___________ is true. At each step we have to _________________. The justification is something that is true, like h H h.

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Unit 3 Section 3

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  1. Unit 3 Section 3 Logic: Intro to Proofs

  2. If we want to prove a conditional statement is true, we start with the __________ and step-by-step, we show that the ___________ is true. At each step we have to _________________. The justification is something that is true, like • h • H • h antecedent consequent justify our conclusion Properties Definitions Postulates Theorems

  3. Example 1 T Given: M is the midpoint of XT. Prove: XM TM Think of this as a conditional statement, with the given as the antecedent and what you want to prove as the consequent: ________________________________. Where have you seen this before? This is one direction of the _____________________. M X If M is the midpoint, then XM TM definition of the midpoint

  4. Example 1 T Given: M is the midpoint of XT. Prove: XM TM So a proof of this might look like this: M X Given Definition of a midpoint

  5. Example 2 C Given: m CAT = 60° Prove: CAT is acute A T Given m CAT = 60° Definition of an acute angle CAT is acute

  6. Example 3 Now let’s go further: Given: m TAX = 120° Prove: CAT is acute C A T X Given Given Definition of a straight angle Angle Addition Postulate Substitution Property Addition Property of Equality Definition of an acute angle

  7. You were already doing problems like finding the measure of CAT, without realizing how many steps you were thinking through as you did them! The trick to doing _________ is to break down the thinking and to make sure that each step is a logical conclusion of things you already have written down. Now let’s prove our first theorem – something we have already observed in angle problems we’ve done. The Vertical Angles Congruence Theorem says “If two angles are vertical, then they are congruent.” To prove this, we assume that the _______________. That is we have a _________________. We try to prove they are congruent. proofs antecedent is true vertical angle pair

  8. Example 4 Given: 2 and 4 are vertical angles Prove: 2 4 1 2 4 3 2 & 4 are vertical angles Given Linear Pairs are supplementary 1 + 4 = 180° Linear Pairs are supplementary 1 + 2 = 1 + 4 Substitution Property 2 = 4 Addition Property of Equality 2 4 Definition of Congruence

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