2.6 Proving Statement 2.6 Proving Statement about Anglesabout Angles

Congruent Supplement TheoremCongruent Supplement Theorem

Congruent Complement TheoremCongruent Complement Theorem

Vertical Angle TheoremVertical Angle Theorem

Theorem 2.2 Properties of Angle Congruence

Reflexive:

Symmetric:

Transitive:

AA

ABthenBAIf ,

CAthenCBBandAIf ,

Theorem 2.3

All right angles are Congruent.

Prove it

Theorem 2.3 All right angles are Congruent.

#1. are right angles #1. Given

#2. and

#2.Def. of Right angles

#3. 90 = 90 #3. Reflexive Prop.

#4. #4. Substitution

#5. #5. Def of congruent

BAand

90Am 90Bm

BmAm

BA

Theorem 2.4 Congruent Supplements Theorem

If 2 angles are supplementary to the same

( or congruent angles), then they are congruent to each other.

Theorem 2.4 Congruent Supplements Theorem

If 2 angles are supplementary to the same

( or congruent angles), then they are congruent to each other.

1 2 3 2

If and are supplementary,

then are congruent Supps. of ≌ angles are ≌

21 and 23 and

31 and

Theorem 2.5 Congruent Complements Theorem If 2 angles are complementary to the same

( or congruent angles), then they are congruent to each other. 1 3

2 2

If and are complementary,

then are congruent Comps. of ≌ angles are ≌

21 and 23 and

31 and

Postulate 12

Linear Pairs are supplementary.

Vertical Angles Theorem

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."

http://en.wikipedia.org/wiki/Thales

Vertical Angles Theorem

Vertical Angles are Congruent

42;31

Solve for x and y

HomeworkHomework

Page 113 – 115 Page 113 – 115

#10 – 22, 24#10 – 22, 24

HomeworkHomework

Page 114 – 115Page 114 – 115

##23, 25 - 28,23, 25 - 28,

30, 33 - 36,30, 33 - 36,

42 - 4542 - 45