Download 2.5 Proving Angles Congruent SWBAT…

2.5 Proving Angles Congruent
SWBAT…
• Identify angles
• To prove and apply theorems about angles
Definitions
Vertical angles: two angles whose sides form two
pairs of opposite rays
Adjacent angles: two coplanar angels with a
common side, a common vertex, and no common
interior points.
Complementary angles: two angles whose measures
have sum 90
Supplementary angels: two angles whose measures
have sum of 180
Id angles pairs
•
In the diagram identity pairs of numbered
angles that are related as follows.
a. Complementary
b. Supplementary
c. Vertical
2
1
5
3
4
FYI
• Things we can conclude from a diagram
• Adjacent angles
• Adjacent supplementary angles
• Vertical angles
• Things we can NOT conclude
• Angels or segments are congruent
• An angle is a right angle
• Lines are parallel or perpendicular
Supplemental Theorem
• If two angles form a linear pair, then they
are supplementary
Complement Theorem
• If the noncommon sides of two adjacent
angels form a right angle, then the angles
are complimentary angles.
Theorem 2-2
• If two angles are supplements of the same
angle (or of congruent angles), then the two
angels are congruent.
• If m<1 + m<2 = 180 and m<2 + m<3 = 180
then m<1 = m<3
Example 3: Proof of Theorem 2.2
• Given <1 and <2 are supplementary
<2 and <3 are supplementary
• Prove: <1 = <3
•
1.
2.
Statements
<1 and <2 are
supplementary; <2 and
<3 are supplementary
m<1 + m<2 = 180
m<2 + m<3 = 180
3.
4. m<1 = m<3
5. <1 congruent <3
1.
Given
2.
3. Substitution
4.
5.
Theorem 2-3
• Angles complementary to the same angle or
to congruent angles are congruent