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Section 3.4

Section 3.4. Types of Proofs. Theorems. Thm 3.3: If two lines are perpendicular, then they intersect to form four right angles. Thm 3.4: All right angles are congruent. Thm 3.5: If two lines intersect to form a pair of adjacent congruent angles, then the lines are perpendicular.

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Section 3.4

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  1. Section 3.4 Types of Proofs

  2. Theorems • Thm 3.3: If two lines are perpendicular, then they intersect to form four right angles. • Thm 3.4: All right angles are congruent. • Thm 3.5: If two lines intersect to form a pair of adjacent congruent angles, then the lines are perpendicular

  3. Types of Proofs • Two Column • Every statement has a corresponding reason • Written in logical order • All lines numbered • Most organized looking of all proofs

  4. m n Ex: Two Column Proof 1 2 Given : <1  <2;<1 & <2 are a linear pairProve: m  n Statements Reasons • <1≌<2 1. Given • m<1= m<2 2. def of congr <‘s • <1 and <2 are a linear pair 3. given • m<1 + m<2 = 180° 4. linear pair post • m<1 + m<1 = 180° 5. subst • 2(m<1) = 180° 6. distrib • m<1= 90° 7. div • <1 is a right angle 8. def of right < • Line n and m are perp 9. def of perp lines

  5. Paragraph Proof • Written as a narrative; without columns • Not easy to use w/ more involved proofs • Connects statements and corresponding reasons with words such as: by, because, and since

  6. Ex of Paragraph proof Given: <3 ≌ <4 Prove:<1 + <5 = 180° -<1 and <2 are supps and <4 and <5 are supps b/c all linear pairs are supples -<1 + <2 = 180° and <4 + <5= 180° y def of supples <‘s -<1 ≌ <3 since vert <‘s are ≌ -<1 + <5 = 180° by subst

  7. Flow Proof • Uses arrows to show the “flow” of the logical proof • Corresponding reasons are written below each statement(which are in boxes) • Not feasible for involved proofs, generally used for short, simple proofs • Some steps may be implied and not shown

  8. Ex of Flow Proof Given: <1 ≌ <3 Prove: <QPS ≌ <TPR

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