1. 2.6 Proving Statement about Angles
Congruent Supplement Theorem
Congruent Complement Theorem
Vertical Angle Theorem

2. Theorem 2.2 Properties of Angle Congruence
Reflexive:
Symmetric:
Transitive:

3. Theorem 2.3
All right angles are Congruent.
Prove it

4. Theorem 2.3 All right angles are Congruent.
# are right angles #1. Given
# and
#2.Def. of Right angles
#3. 90 = 90 #3. Reflexive Prop.
#4. #4. Substitution
#5. #5. Def of congruent

5. Theorem 2.4 Congruent Supplements Theorem
If 2 angles are supplementary to the same
( or congruent angles), then they are congruent to each other.

6. Theorem 2.4 Congruent Supplements Theorem
If 2 angles are supplementary to the same
( or congruent angles), then they are congruent to each other.
If and are supplementary,
then are congruent
Supps. of ≌ angles are ≌

7. Theorem 2.5 Congruent Complements Theorem
If 2 angles are complementary to the same
( or congruent angles), then they are congruent to each other.
If and are complementary,
then are congruent
Comps. of ≌ angles are ≌

8. Postulate 12
Linear Pairs are supplementary.

9. Vertical Angles Theorem

10. Vertical Angles Theorem
The oldest known Proof.
Thales of Miletus gave us the first glimpse of the vertical angle theorem.
Thales of Miletus ( Greek: , Thalēs; c. 624 BC – c. 546 BC) was a pre-Socratic Greek philosopher from Miletus in Asia Minor, and one of the Seven Sages of Greece. Many, most notably Aristotle, regard him as the first philosopher in the Greek tradition.1 According to Bertrand Russell, "Western philosophy begins with Thales."

11. Vertical Angles Theorem
Vertical Angles are Congruent

12. Solve for x and y

13. Homework
Page 113 – 115
#10 – 22, 24

14. Homework
Page 114 – 115
# 23, ,
30, ,