Download Beginning Proofs

Beginning Proofs
Lesson 1.4
Two column proofs and theorems
Theorem: A mathematical statement that
can be proven.
We prove theorem(s)
We shall omit the proofs of certain theorems, even though all have
proofs
We use theorems to help prove sample
problems
You are then given the challenge of using
the theorems to prove homework
problems. Theorems will save you much
time if you learn them and then use them!
You use theorems to prove others,
Do not use proffs of theorems as a guide.
Use sample problems as a guide.
You use deductive reasoning to prove
theorems. (Basically you create a chain of
logical steps that move from the hypothesis
to the concusion of the conjecture you are
proving
Theorem 1: If two angles are right angles, then they
are congruent
Given: <A is a right <
<B is a right <
Prove: <A  <B
Proof:
Statements
Reasons
1.
2.
3.
4.
5.
1. Given
2. Right angles = 90
3. Given
4. Right angles = 90
5. Two angles of the same
measure are congruent
<A is a right angle
M<A = 90
<B is a right angle
M<B = 90
<A  <B
Theorem 2: If two angles are
straight angles, then they are
congruent.
Given: Diagram
Prove: <ABC <FBD
Given: <ABC = 115
<XYZ = 115
Prove: <ABC  <XYZ
Statements
1. <ABC = 115
2. <XYZ = 115
3.
<ABC  <XYZ
Reasons
1. Given
2. Given
3. Def of
 angles
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