4-7 Vertical Angles
Vertical angle definition
•Two angles are vertical angles if their sides formtwo pairs of opposite rays.
•1 and 2 are vertical angles
Vertical angle theorem
•Vertical angles are congruent
•Create a sketch
•Write the given and the prove
•Given: 1 and 2 are a vertical angles
•Prove: 1 2
Vertical angle theorem
•Vertical angles are congruent
Statements
Reasons
1. 1 and 2 are vertical angles
Given
2.
Def of vertical angles
3.1 and 3 form a linear pair2 and 3 form a linear pair
Def of linear pair
4.1 is supplementary to 32 is supplementary to 3
Supplement Postulate
5.3 3
Reflexive prop
6.1 2
Supplement Theorem
Q.E.D.
Perpendicular Lines theorem
•If 2 lines are perpendicular they form four rightangles
•Create a sketch
•Write the given and the prove
•Given: L1 L2
•Prove: 1, 2, 3, 4 are right angles
1
2
3
4
L2
L1
Perpendicular Lines theorem
•If 2 lines are perpendicular they form four right angles
Statements
Reasons
1. L1 L2
Given
2. 1 is a right angle
Def of perpendicular
3.m1 = 90
Def. of right angle
4.1 and 2 are a linear pair
Given sketch
5.1 and 2 are a supplementary
Supplement Postulate
6.m1 + m2 = 180
Def of suppl.
7.90 + m2 = 180
Substitution 2 into 6
8.m2 = 90
Subtraction prop. of eq.
9.m3 = 90
Vertical Angle Theorem
10.m4 = m90
Vertical Angle Theorem
Q.E.D.
Homework
•Pg. 106 – 108: #2 - 10. In 10, note that theproblem is discussing two situations.
•Pg. 109 #1, 2