Download Bell-ringer SECTION 2.4: THEOREMS ABOUT ANGLES Examples

2/19/2015
Bell-ringer
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Solve this equation for x and justify your steps.
3(x-4)=2(x+8)
SECTION 2.4: THEOREMS
ABOUT ANGLES
Examples:
Definition of Complementary Angles
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Two angles whose measures have the sum 90
degrees.
They do not have to be adjacent.
Each angle is called the complement of the other
R
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<A =4x+17 and <B=5x+3. <A and <B are
complementary. What is x?
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Angle 1 is twice as big as it’s complement. How big
is angle 1?
X
60º
W
50º
30º
S
T
<R and <T are complements
40º
Y
Z
<XYW and <WYZ are complements
Complementary Angles Theorem
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If 2 angles are complements of congruent angles
(or the same angle), then the 2 angles are
congruent.
Given: <1 and <2 are complements and <2 and
<3 are complements.
Prove: m<1=m<3
Definition of Supplementary Angles
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Two angles whose measures have the sum 180
degrees
Each angle is called a supplement of the other.
50º
A
130º
B
G
<A and <B are supplementary
(180-x)º xº
D
E
F
<DEG and <GEF are supplementary
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Examples:
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Supplementary Angles Theorem
A supplement of an angle is three times as large as
a complement of the angle. Find the measure of
the angle.
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<A=6x+25 and <B=2x-5. <A and <B are
supplementary. What is the measure of <A?
Vertical Angles
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Vertical Angles Theorem
Two angles such that the sides of the one angle are
opposite rays to the sides of the other angle.
Angles that are opposite each other when 2 lines
intersect.
<1 and <4 are vertical angles
<2 and <3 are vertical angles
3
1
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Vertical Angles are congruent
Given: <1 and <4 are vertical
Prove: m<1=m<4
3
1
4
2
4
2
Classwork
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If 2 angles are supplements of congruent angles (or
of the same angle), then the two angles are
congruent.
Given: <1 and <2 are supplements and <2 and <3
are supplements.
Prove: m<1=m<3
Pg 51-52 Classroom Exercises #1-4, 10-19
Work with a partner or group of 3 on these
problems.
Homework
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pg 52 written exercises #1-21 odd
2