Download 2-5 Notes

GEOMETRY
2-5
NOTES
AUGUST 26, 2016
OR
AUGUST 29, 2016
2-5 PROVING ANGLES CONGRUENT
• Learning Objectives
• Identify angle pairs
• Understand and use theorems about angles
• Vertical Angles
• Two angles whose sides are opposite rays
• Adjacent Angles
• Two coplanar angles with a common side, a common
vertex, and no common interior points
2-5 PROVING ANGLES CONGRUENT
• Complementary Angles
• Two angles whose measure have a sum of 90°. Each angle
is called the compliment of the other.
20°
70°
• Supplementary Angles
• Two angles whose measures have a sum of 180°. Each
angle is called the supplement of the other.
35°
𝟏𝟕𝟓°
2-5 PROVING ANGLES CONGRUENT
• From a diagram you CAN assume:
• Adjacent angles
• Adjacent supplementary angles
• Vertical angles
• Unless the diagram gives you this information, you
CANNOT assume :
• Angles or segments are congruent
• An angle is a right angle
• Lines are parallel or perpendicular
• And NEVER assume that anything is drawn to scale
unless you are specifically told to use a ruler or
protractor to measure
2-5 PROVING ANGLES CONGRUENT
• Proof • The set of steps you take to reach a
theorem
• Theorem • The statement that you prove true
• Theorem 2-1:
• Vertical Angles Theorem
• Vertical angles are congruent
∠1≅∠2
and
∠3≅∠4
1
3
4
2
2-5 PROVING ANGLES CONGRUENT
• Theorem 2-2:
• Congruent Supplements Theorem
• If two angles are supplements of the same
angle (or of congruent angles), then the
two angles are congruent.
Proof on pg. 99
2-5 PROVING ANGLES CONGRUENT
• Theorem 2-3:
• Congruent Complements Theorem
• If two angles are complements of the
same angle (or of congruent angles), then
the two angles are congruent
• Theorem 2-4:
• All right angles are congruent
• Theorem 2-5:
• If two angles are congruent and
supplementary, then each is a right angle
HOMEWORK
2-5
Pg. 100
# 1-18, 20-25, 39-42