1. Proofs about
Segments and Angles
2 column
proofs

2. 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

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

4. 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

5. 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

6. ( ) 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

7. 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

8. 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

9. 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

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