Chapter Two:  
Reasoning and Proof

Geometry   Notes

Chapter  2

Section  2.1
Section  2.2
Section  2.3
Section  2.4
Section  2.5

Geometry Contents

Take notes on the following topics.

Section 2-5  Proving Angles Congruent

Vocabulary

Vertical angles (p. 96) Vertical angles are two angles with sides that are opposite rays.

Adjacent angles (p. 96) Adjacent angles are two coplanar angles that have a common side and a common vertex but no common interior points.

Complementary angles (p. 96) Two angles are complementary angles if the sum of their measures is 90 degrees.

Supplemental angles (p. 98) Two angles are supplementary if the sum of their measures is 180.

Theorem (p. 98) A theorem is a conjecture that is proven.

Paraagraph Proof (p. 100) A proof is a convincing argument that uses deductive reasoning. A proof can be written in many forms.  In a paragraph proof, the statements and reasons are connected in sentences. 

 

Theorem 2-1 Vertical Angles Theorem

Vertical angles are congruent.

Theorem 2-2 Congruent Supplements Theorem

If two angles are supplements of the same angle (or congruent angles), then the two angles are congruent.

Theorem 2-3 Congruent Complements Theorem

If two angles are complements of the same angle (or congruent angles), then the two angles are congruent.

Theorem 2-4

All right angles are congruent

Theorem 2-5

If two angles are congruent and supplementary, then each is a right angle.