Proving Angle
Relationships
Chapter 2 Section 8
Angle Addition Postulate
1
EXAMPLE
Using the Angle Addition Postulate
75
Find the measure of each numbered angle and name the theorem that
justifies your work.
They are a linear pair, so they
will add to 180. Solve for x.
Angles 1 and 2 add to 90.
All angles add to 180. Solve for x.
Angles 11 and 13 add to 180.
Properties of Congruent
Angles
 Reflexive Property
∠A≅∠A
 Symmetric Property
 If ∠ A ≅ ∠ B, then ∠ B ≅ ∠ A
 Transitive Property
 If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C

6
Theorem 2.4:Congruent Supplements
Theorem
 If two angles are supplementary to the same angle
(or to congruent angles), then they are congruent.
Theorem 2.5:Congruent
Complements Theorem
 If two angles are complementary to the same angle
(or to congruent angles), then they are congruent.
Theorem 2.8 Vertical Angles
Theorem
 Vertical angles are congruent.
2
1
3
4
 1 ≅  3;  2 ≅  4
Example – Using Vertical Angles
Theorem
Find the value of x
4x
3x + 35
What is each angle measure?
Set 4x = 3x + 35
Solve for x
Right Angle Theorems
More right angle theorems
Have a great day! 