Right Angle Congruence Theorem
All right angles are congruent.
If ∠ 1 and ∠ 2 are right angles then ___________.
Congruent Supplements Theorem
If two angles are supplementary to the same angle,
then _______ _____ ____________________.
If ∠ 1 and ∠ 2 are supplementary and ∠ 3 and ∠ 2
are supplementary, then ___________________
Congruent Complements Theorem
If two angles are complementary to the same
angle, then _______ _____ _________________.
If ∠ 4 and ∠ 5 are complementary and ∠ 6 and
∠ 5 are complementary, then _________________
Vertical Angles Congruence
Theorem
Vertical angles are congruent.
∠ 1 and ∠ 3 are vertical angles, then ___________
∠ 4 and ∠ 2 are vertical angles, then ___________
Linear Pair Postulate
If two angles form a linear pair, then ________
_____ ______________________.
∠ 1 and ∠ 2 form a linear pair, so ∠ 1 and ∠ 2 are
_______________________ and
_________________________________
1.) Given: ∠ 1 and ∠ 2 are supplements
∠ 1 and ∠ 4 are supplements
m ∠ 2 = 45°
Prove: m ∠ 4 = 45°
1
2
3
2.)
Given: ∠ 2 ≅ ∠ 3
Prove: ∠ 1 ≅ ∠ 4
1
2
Reasons
1.
Statements
Reasons
1.
1.
2. m ∠ 1 + m ∠ 2 = 180
m ∠ 1 + m ∠ 4 = 180
2.
2.
2. Vertical ∠ ’s
3.
3.
4.
4. Vertical ∠ ’s
3. m ∠ 1 + m ∠ 2 = m ∠ 1 + m ∠ 4 3.
4.
5. m ∠ 4 = 45°
5.
4
4
Statements
1. ∠ 1 and ∠ 2 are supplements
∠ 1 and ∠ 4 are supplements
m ∠ 2 = 45°
4. m ∠ 2 = m ∠ 4
3
Theorem
Theorem
Statements and Reasons for Proofs . You need to put them in the proper order.
Definition of Supplementary angles
∠ 1 and ∠ 2 are supplements
∠ 1 and ∠ 4 are Supplements
∠ 2 =45
m∠ 1 + m∠ 2 = m∠ 3 + m∠ 4
m∠ 2 = m∠ 4
Substitution Property of Equality (2x)
Subtraction Property of Equality
m ∠ 1 + m ∠ 2 = 180
m ∠ 1 + m ∠ 4 = 180
Given
Vertical Angles Theorem (2x)
Transitive Property of Congruency (2x)
Given
∠1 ≅ ∠2
∠3 ≅ ∠4
∠1 ≅ ∠4
∠2 ≅ ∠4
∠2 ≅ ∠3