Unit 2 Part 2 Statement and Reason Proofs

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

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

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

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

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

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

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

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

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