Download Chapter 2: Geometric Reasoning

Chapter 2: Geometric Reasoning
Learning Goal:
I can identify properties of equality and congruence.
I can prove theorems about lines and angles using deductive reasoning and a two
column proof.
LESSON 2-5: ALGEBRAIC PROOFS
A proof is an argument that uses logic, definitions, properties,
and previously proven statements to show that a conclusion is
true.
An important part of writing a proof is giving justifications to show
that every step is valid.
Chapter 2: Geometric Reasoning
Like algebra, geometry also uses numbers, variables, and
operations. For example, segment lengths and angle
measures are numbers. So you can use these same
properties of equality to write algebraic proofs in geometry.
Chapter 2: Geometric Reasoning
LESSON 2-6: GEOMETRIC PROOFS
When writing a proof, it is important to justify each
logical step with a reason. You can use symbols and
abbreviations, but they must be clear enough so that
anyone who reads your proof will understand them.
A theorem is any statement that you can prove.
Once you have proven a theorem, you can use it as a
reason in later proofs
Chapter 2: Geometric Reasoning
Definition of Midpoint
Definition of Segment Bisector
Definition of Angle Bisector
Chapter 2: Geometric Reasoning
Definition of Complementary Angles
Definition of Supplementary Angles
Definition of Linear Pairs
Definition of Right Angles
Definition of Straight Angles
Definition of Congruent Angles
Definition of Congruent Segments
Vertical Angles are Congruent
Chapter 2: Geometric Reasoning
A geometric proof begins with Given and Prove statements, which
restate the hypothesis and conclusion of the conjecture. In a twocolumn proof, you list the steps of the proof in the left column.
You write the matching reason for each step in the right column.
TWO COLUMN PROOFS:
Given:
Prove:
Statement:
Reason:
1.
1.
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.