Unit 2 Part 2

1. Unit 2 Part 2 Statement and Reason Proofs

2. Two Column Proof • Statement | Reason • 1st Statement | Reason • 2nd Statement | Reason • etc…

3. Here are SOME of the reasons. • Addition Property • Subtraction Property • Multiplication Property • Division Property • Substitution Property • Distributive Property

4. Given: -4(11x + 2) = 80 Prove x=-2 • Statement | Reason • -4(11x + 2) = 80 | Given • -44x – 8 = 80 | distributive property • -44x = 88 | addition property • x = -2 | division property

5. More reasons • Reflexive Property • Example AB=AB or ∠A = ∠A • Symmetric Property • Example C = D then D = C • Transitive Property • If A = D = G, then A = G

6. More reasons • Segment Addition Postulate • Example AB + B C = AC • Angle Addition Postulate • Example ∠ ABC + ∠ CBD= ∠ ABD • Definition of Vertical Angles • Definition of Supplementary Angles • Definition of Complementary Angles

7. Given 3(x-2) = x + 4 prove x=5 Statement Reason Given Distribution Prop. Subtraction Prop. Addition Prop. Division Prop.

8. Given WY = XZ prove WX = YZ W X Y Z Statement Reason WY = XZ Given WY= WX + XY Segment Addition Post. XZ = XY + YZ Segment Addition Post. WX + XY = XY + YZ Substitution Prop. WX = YZ Subtraction Prop.

9. Prove angle ABC = angle DBE • Given ∠ ABD = ∠ CBE C D A Statement Reason E ∠ ABD = ∠ CBE Given B ∠ABD = ∠ABC + ∠CBD Angle Addition Post. ∠CBE = ∠CBD + ∠DBE Angle Addition Post. Substitution Prop. ∠ABC + ∠CBD = ∠CBD + ∠DBE ∠ ABC = ∠ DBE Subtraction Prop.

10. These are difficult, but practice, practice, practice, practice…..