Download Proving Angle Relationships Objective

October 10, 2014
(2.8) Proving Angle Relationships
Objective: Write proofs involving angles (supplementary,
complementary, congruent, and right).
Why: Construct viable arguments.
October 10, 2014
Obj:
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
Protractor Postulate:
Given any angle, the measure can be put into one-to-one
correspondence with real numbers between 0 and 180.
60
110
50
40
90
80
70
90
100
80
C
110
120
70
120
130
60
130
140
50
140
30
100
40
0°
150
150
30
160
20
160
10
A
0
20
10
170
180
0
B
Angle Addition Postulate:
If D is in the interior of
then m
ABD + m
ABC,
DBC = m
170
180
A
D
ABC
B
C
October 10, 2014
(2.8)
Obj:
EX.
Find m
ABD if m
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
ABC = 90o. Justify each step.
A
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s
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le
p
t
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o
C
t
e
k
c
a
p
s
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h
t
e
(8x+1)o
D
(5x-2)o
B
Tak
October 10, 2014
Obj:
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
Supplement Theorem:
If 2
s form a linear pair, then they are supplementary.
Complement Theorem:
If the noncommon sides of two adjacent angles form a right
angle, then the angles are complementary angles.
October 10, 2014
Obj:
Ex.
6 and
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
7 form a linear pair. If m
m 7 = 5x + 12, find x, m
6, and m
6 = 3x + 32 and
7. Justify each step.
October 10, 2014
Obj:
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
Congruent Supplements Theorem:
s suppl. to same
2
or
s are = .
=
1
3
Congruent Complements Theorem:
s compl. to same
or =
s are =
.
October 10, 2014
Obj:
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
(Proof): One Case of the Congruent Complements Theorem
If 2 angles are complementary to the same angle, then
they are congruent to each other.
Given:
Prove:
Statements
Reasons
October 10, 2014
Obj:
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
Vertical Angles Theorem:
Vert.
s are = .
B
A
Ex.
Given: DB bis.
Prove:
2 =
ADC
3
1 2
D
3
C
October 10, 2014
October 10, 2014
October 10, 2014
Right Angle Theorems:
Obj:
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
1. Perpendicular lines interest to form 4 right angles.
2. All right angles are congruent.
3. Perpendicular lines form congruent adjacent angles.
4. If two angles are congruent and supplementary, then each angle
is a right angle.
5. If two congruent angles form a linear pair, then they are right
angles.
October 10, 2014
Obj:
Given:
ABC is a right angle.
Prove:
ABD and
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
A
D
CBD are complementary
B
Statement
Reason
C
October 10, 2014
Obj:
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
HW:
(HR) (2.8) Pg. 156: 10, 13, 15, 16, 21, 25