Proving Angle Proving Angle RelationshipsRelationships

Chapter 2 Section 8

Angle Addition Postulate

11 EXAMPLEEXAMPLE Using the Angle Addition Postulate

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Find the measure of each numbered angle and name the theorem that justifies your work.

They are a linear pair, so theywill add to 180. Solve for x. All angles add to 180. Solve for x.

Angles 1 and 2 add to 90.Angles 11 and 13 add to 180.

6

Properties of Congruent AnglesReflexive Property ∠ A ≅ ∠ ASymmetric PropertyIf ∠ A ≅ ∠ B, then ∠ B ≅ ∠ ATransitive Property If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C, then ∠ A ≅ ∠ C

Theorem 2.4:Congruent Supplements Theorem

If two angles are supplementary to the same angle (or to congruent angles), then they are congruentcongruent.

Theorem 2.5:Congruent Complements Theorem

If two angles are complementary to the same angle (or to congruent angles), then they are congruentcongruent.

Theorem 2.8 Vertical Angles Theorem

Vertical angles are congruent.

1

23

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 + 35Solve for x

Right Angle Theorems

More right angle theorems

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