Download 2-5 Proving Angles Congruent M11.B.2 2.5.11.C

2-5 Proving Angles Congruent
M11.B.2 2.5.11.C
OBJECTIVES:
1) TO IDENTIFY ANGLE PAIRS
2) TO PROVE AND APPLY THEOREMS ABOUT
ANGLES
Vocabulary
 Vertical Angles – two angles whose sides form two
pairs of opposite rays
1
3
4
2
 Adjacent Angles – two coplanar angles with a
common side, a common vertex, and no common
interior points
1 2
Vocabulary
 Complementary Angles – two angles whose
measures have sum 90°. Each angle is called the
complement of the other.
A 60
B 30
 Supplementary Angles – two angles whose measures
have sum 180°. Each angle is called the supplement
of the other.
3 4
75
105
Example: Identifying Angle Pairs
2
1
3
4
• Name all pairs of angles
a) Vertical:
b) Supplementary:
c) Complementary:
Example: Identify Angle Pairs
 Complementary:
 Supplementary:
 Vertical:
2
1
5
3
4
Assumptions from Diagram
**Things you can conclude from a diagram:
1) Adjacent angles
2) Adjacent supplementary angles
3) Vertical angles
Can NOT Assume: (Unless Marked)
**Things you cannot conclude from a diagram without
markings
1) Angles or segments are congruent
2) An angle is a right angle
3) Lines are parallel or perpendicular
Example: Making Conclusions from a Diagram
True or False
1) < 3 is a right angle
2) < 1 and < 5 are adjacent
3) < 3 = < 5
4
3
2
5 1
Vertical Angle Theorem
 Vertical angles are congruent.
Example: Find the value of x
2x - 3
4x - 10