Beginning Proofs

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Lesson 1.4 Beginning Proofs
Objective Write simple two-column proofs
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Introducing
The Two-Column Proof! The two-column proof is
the major type of proof we use throughout our
studies. Def. A theorem is a mathematical
statement that can be proved.
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Theorem Procedure

1. We present a theorem(s).
2. We prove the theorem(s).
3. We use the theorems to help prove sample
   problems.
4. You use the theorems to prove homework problems.
   

Note The sooner you learn the theorems, the
easier your homework will be! ?
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Theorem 1
If two angles are right angles, then they are
congruent.
Given ltA is a right lt. ltB is a right
lt. Prove
B
A
Statement Reason
1. ltA is a right lt
1. Given
2. mltA 90
2. If an lt is a right lt then its measure is 90
3. ltB is a right lt
3. Given
4. If an lt is a right lt then its measure is 90
4. mltB 90

1. If 2 lts have the same measure then they are
   congruent.

5.
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Theorem 2
If two angles are straight angles, then they are
congruent.
U
Given ltNAU is a straight lt. ltPHS is
a straight lt. Prove
A
N
P
H
S
Statement Reason
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Practice Makes Perfect
Now that we know the two theorems (and have
proved them), we apply what we know to sample
problems. about what we can and cannot assume
from a diagram! This is important with proofs!
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Example 1
Given ltRST 50 ltTSV 40
ltX is a right angle Prove
R
T
X
S
V
Statement Reason
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Example 2
X
Y
Given ltABD 30 ltABC 90
ltEFY 50 20 ltXFY 9
40 Prove
D
A
F
E
B
C
Statement Reason
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Homework
Lesson 1.4 Worksheet