Download 2-4 Special Pairs of Angles

2-4 Special Pairs of Angles
Objectives
-Supplementary Angles
Complementary Angles
-Vertical angles
Complementary Angles
• Are two angles whose measures have the sum
90. Each angle is called the complement of
the other.
A
60⁰
30⁰
C
Supplementary Angles
• Are two angles whose measures have the sum
180. Each angle is called a supplement of the
other.
Vertical Angles
• Are two angles such that the sides of one
angle are opposite rays to the sides of the
other angle. When two lines intersect, they
form two pairs of vertical angles.
Theorem:
Any pair of
vertical angles
are congruent.
Vertical Angles
When two lines intersect, 4 angles are made, angles that are
opposite of one another are VERTICAL ANGLES
Theorem
• Vertical angles are congruent
– Given:  1 and  2 are vertical angles
– Prove: 1  2
1.  1 and  2 are vertical angles
1. Given
3
1
2
2x + 2
100
2
1
2x + 5
x + 100
ANGLE 1 and ANGLE 2 are CONGRUENT
FIND m<1
• Angle 1 and angle 2 are supplementary. Find the
m<1 and m<2, if m<1=2x+30 and m<2=3x+40.
Homework
• Pg. 52
• 1-6, 13-24, 27