# Prove Statements about Segments and Angles

```PROVE STATEMENTS ABOUT
SEGMENTS AND ANGLES
Section 2.6
Proofs


Proofs are logical arguments that explains why a
statement is true.
Proofs use theorems, postulates, formulas, and
definitions to prove facts to be true.
Theorems


Theorems are statements that can be proven true.
There are many theorems that have already been
proven true that we can use in order to prove
different statements
2 column proofs



Most of the proofs that we will do in this class will
be 2 column proofs
2 column proofs have the steps towards proving a
statement in the first column and the reasons
(postulates, definitions, theorems, and formulas) in
the second column.
We did algebraic 2 column proofs in the last
section.
Algebraic Proof



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

Prove that x = 9 when given 2(x – 7) = 4x – 32
2(x – 7) = 4x – 32
Given
2x – 14 = 4x – 32
Distribution Property
-14 = 2x – 32
Subtraction Property
18 = 2x
9=x
Division Property
Geometric Proof

Given:



Prove:


Point C is in the interior of Angle ABD.
Angle ABD is a right angle.
Angle ABC and Angle CBD are complementary.
2 Column Proof:
Statement
Reason
ABD is a right angle
Given
m
ABD = 90˚
Point C is in the interior of
Def. Right Angle
ABD
Given
m ABD = m ABC + m CBD