Download October 12, 2015

October 12, 2015
October 12, 2015
October 12, 2015
October 12, 2015
October 12, 2015
(2.8) Proving Angle Relationships
Objective: Write proofs involving angles (supplementary,
complementary, congruent, and right).
Why: Construct viable arguments.
October 12, 2015
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.
80
70
60
110
50
40
100
90
90
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 12, 2015
(2.8)
Obj:
EX.
Find m
ABD if m
A
(8x+1)o
D
(5x-2)o
B
C
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
ABC = 90o. Justify each step.
October 12, 2015
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 12, 2015
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 12, 2015
October 12, 2015
Obj:
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
Congruent Supplements Theorem:
s suppl. to same
2
or =
1
s are =
.
3
Congruent Complements Theorem:
s compl. to same
or =
s are=
.
October 12, 2015
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 12, 2015
October 12, 2015
Vertical Angles Theorem:
Vert.
Obj:
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
s are = .
Proof:
D
A
Given: diagram as shown
Prove:
ABC =
Statement
B
C
DBE
Reason
E
October 12, 2015
Obj:
Ex.
B
A
Given: DB bis.
ADC
Prove:
3
2 =
Statement
1 2
D
Reason
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
3
C
October 12, 2015
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 12, 2015
Obj:
Given:
ABC is a right angle.
Prove:
ABD and
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
A
CBD are complementary
D
B
Statement
Reason
C
October 12, 2015
Obj:
Write proofs involving angles (supplmentary,
complementary, congruent, and right).
HW:
(HR) (2.8) Pg. 156: 10, 13, 15, 16, 21, 25