Download PPSection 2.5

Geometry: Section 2.5
Proving Statements about Segments and
Angles
What you will learn:
1. Write two column proofs
2.Name and prove properties of congruence
A proof is a logical argument that uses
deductive reasoning to show that a statement
is true.
A two-column proof has numbered
statements and corresponding reasons that
show an argument in logical order.
In the left hand column, we will have statements
which lead from the given information to the
conclusion which we are proving. In the right hand
column, we give a reason why each statement is
true. Since we list the given information first, our
Given Any other
first reason will always be ___________.
reason must be a _________________,
Definition
_________________,
_________________
or
Property
Postulate
______________.
Theorem
A theorem is a statement that can be proven.
1. m1  m3
1. Given
2) m1  m2  mCBE
m2  m3  mDBA
2) Angle Addition Postulate
3) m3  m2  mCBE
3) Substitution Property
4) mDBA  mEBC
4) Substitution Property
1) 1 and 3 are supplementary
2 and 3 are supplementary
1) Given
2) m1  m3  180
m2  m3  180
2) Def. of supp.
3) m1  m3  m2  m3
3) Subst. Prop.
4) 1  2
4) Subtraction Prop.
In section 2.4, we looked at the Reflexive,
Symmetric and Transitive Properties of
Equality. Out first theorems deal with
Properties of Segment Congruence and
Properties of Angle Congruence.
I will allow you to simply refer to these
as the Reflexive, Symmetric and
Transitive Properties without expecting
you to distinguish between segments
and angles.
Example: Name the property that justifies each
statement.
Reflexive Property
Transitive Property
or Substitution Property
HW: p103 / 3 -10, 14