2.6 2.7 Proofs about Segments and Angles 2 column proofs

a conjecture that you can prove. Theorem - a conjecture that you can prove. Paragraph Proof- is written in complete sentences. It uses statements and reasons. see p. 124 fguilbert

-information you are GIVEN. The hypothesis -information you are GIVEN. The conclusion - statement you wish to PROVE. fguilbert

P 104 C E D G: m1 = m3 A P: mEBA =mDBC B Put tic marks 1 2 3 A P: mEBA =mDBC B Put tic marks for given info. fguilbert

C E D A B given Subst. 1 2 3 G: m1 = m3 P: mEBA =mDBC 1 2 3 A Statements Reasons B m1 = m3 given m1 +m2 = m3 +m2 Addition Prop m1 +m2 = mDBC m3 +m2 = mEBA Angle Addition mDBC = mEBA Subst. fguilbert

( ) Let’s prove this with a 2 column proof. The Vertical Angle Theorem says that vertical angles are congruent 1 ( ) 2 4 3 Let’s prove this with a 2 column proof. fguilbert

List your steps in logical order. Give a reason for each step. 1 Given: Prove: 1 and3 are vertical angles 1 = 3 2 4 3 Think of a strategy. List your steps in logical order. Give a reason for each step. fguilbert

1 Statements Reasons 2 4 1.  1and3 1. given 3 1+2=180 2+3=180 are vertical s 1. given 3 1+2=180 2+3=180 2. linear pair 3. substitution 3. 1+2=2+3 4. Subtraction 4. 1 = 3 fguilbert

start with the given info. If you don’t know what to do When writing a proof, start with the given info. If you don’t know what to do next,,,,,,,,,,,, Write all the facts you know. Then think about a strategy. fguilbert

you achieve a happy spirit. When you practice HOPE you achieve a happy spirit. fguilbert