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Geometry
Beginning Proof
Notes/Practice
From yesterdays notes…

If two angles are vertical angles, then their rays are opposite rays.

If their rays are opposite rays, then they form lines.

If they form lines, then they are straight angles.

If they are straight angles, then they have measure of 1800 .

If they have measure of 1800 , then there exists supplementary angles.

If there exists supplementary angles, then we can use the angle addition postulate.
And we can keep going and going…
The idea behind ______________ is that there is reasoning for each of the conclusions we
could make above.
If two angles are vertical angles, then their rays are opposite rays.
Why? _________________________________________________________________
If their rays are opposite rays, then they make lines.
Why? _________________________________________________________________
Proof is using reasoning to formally, systematically show how conclusions can be reached
using previous knowledge.
1.
They are mainly used for proving _____________________________.
a. If – then statements that use definitions, postulates, axioms and
previously proven theorems to show the conclusion is always true.
i. If two angles are complementary, then their measures add up to 90 0
1. Hypothesis is the given
2. Conclusion is what you are proving
b. Done using TWO – COLUMN proofs, that summarize the statements and
conclusions.
TWO – COLUMN PROOF: _______________________________________________________
________________________________________________________________________.
Given: A and B are complementary
Prove: mA+mB=900
STATEMENTS
REASONS
Geometry
Beginning Proof
Notes/Practice
*Reasons can be any definition, axiom, postulate, or theorem that has been proven! We
will be using symbols to describe our reasons, as long as we can
Example 2: If  A and  B are right angles, then they are congruent.
Hypothesis is the GIVEN…Conclusion is the PROVE.
Given:
A is a right angle
B is a right angle
Prove: A  B
STATEMENTS
REASONS
THEOREM PROVED: ____________________________________________________________
____________________________________________________________________________.
Reason in Proof: _________________________________________________
Example 3:
Given: mRST=500
R
T
mTSV=400
X is a right angle
Prove: RSV  X
STATEMENTS
S
X
V
REASONS