Chapter Two:
Reasoning and Proof
Section 2-5:
Proving Angles Congruent
Objectives
To prove and apply theorems about angles.
Vocabulary
Theorem
Proof
Theorem
A theorem is a conjecture that is proven.
We use proofs to show that theorems are
true.
Theorem 2-1:
“Vertical Angles Theorem”
Vertical Angles are Congruent.
Prove Theorem 2-1
Given: 1 and 2 are vertical angles
Prove: 1  2
Statements:
Reasons:
1) m1  m3  180
1)______________
m2  m3  180
2) m1  m3  m2  m3
2)______________
3)____________________
3) Subtraction Property of Equality
4)____________________
4) Definition of Congruence
Proof
A proof is a convincing argument that uses
deductive reasoning.
There are several types of proofs which
include:
Paragraph proofs
Column proofs
Using the Vertical Angles
Theorem
Solve for the values of x:
Theorem 2-2:
“Congruent Supplements
Theorem”
If two angles are
supplements of the same
angle (or of congruent angles) then they are
congruent to each other.
Theorem 2-3:
“Congruent Supplements
Theorem”
If two angles are
complements of the same
angle (or of congruent angles) then they are
congruent to each other.
Theorem 2-4:
All right angles are congruent.
Theorem 2-5:
If two angles are congruent and
supplementary, then each is a right angle.