This document discusses several theorems about angle relationships: the Right Angle Congruence Theorem which states that all right angles are congruent; the Congruent Supplements Theorem which states that if two angles are supplementary to the same angle then they are congruent; the Congruent Complements Theorem which states that if two angles are complementary to the same angle then they are congruent; the Linear Pair Postulate which states that if two angles form a linear pair then they are supplementary; and the Vertical Angles Congruence Theorem which states that vertical angles are congruent. It provides proofs for some of these theorems and examples of how to draw diagrams and write statements to prove the Congruent Complements Theorem. Home

1. 2.7 Prove Angle Pair Relationships September 14, 2011
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HW pg.127 #3­6, 8­26 evens, 37­39 1

2. 2.7 Prove Angle Pair Relationships September 14, 2011
2.7 Prove Angle Pair Relationships
Theorem 2.3: Right Angle Congruence Theorem
All right angles are congruent.
Proof:
Given: <1 & <2 are right angles
Prove: <1 ≅ <2
Statements Reasons
1. <1 & <2 are right <s 1. Given
2. m<1=90, m<2=90 2. Def. of Right Angle
3. m<1=m<2 3. Transitive Prop. of =
4. <1 ≅ <2 4. Def. of ≅ Angles
HW pg.127 #3­6, 8­26 evens, 37­39 2

3. 2.7 Prove Angle Pair Relationships September 14, 2011
Theorem 2.4: Congruent Supplements Theorem
If 2 angles are supplementary to the same angle,
(or ≅ to angles), then they are congruent.
HW pg.127 #3­6, 8­26 evens, 37­39 3

4. 2.7 Prove Angle Pair Relationships September 14, 2011
Theorem 2.5: Congruent Complements Theorem
If 2 angles are complementary to the same angle
(or ≅ to angles), then they are congruent.
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4 6
If <4 & <5 are complementary and <6 & <5 are complementary,
then <4 ≅ <6.
Draw a diagram and write GIVEN and PROVE
statements for a proof of each case of the
Congruent Complements Theorem.
HW pg.127 #3­6, 8­26 evens, 37­39 4

5. 2.7 Prove Angle Pair Relationships September 14, 2011
Postulate 12: Linear Pair Postulate
If 2 angles form a linear pair,
then they are supplementary
Theorem 2.6: Vertical Angles Congruence Theorem
Vertical angles are ≅.
HW pg.127 #3­6, 8­26 evens, 37­39 5

6. 2.7 Prove Angle Pair Relationships September 14, 2011
HW pg.127 #3­6, 8­26 evens, 37­39 6

7. 2.7 Prove Angle Pair Relationships September 14, 2011
HW pg. 127
#3­6,
8­26 evens,
37 & 39
HW pg.127 #3­6, 8­26 evens, 37­39 7