Download write proofs involving supplementary and complementary angles • wr

OBJECTIVES:
• write proofs involving supplementary and complementary
Warm up: p. 106
# 40 ­ 45
angles
• write proofs involving congruent and right angles
Section 2­8
______________
Postulate 2.10 Protractor Postulate
Given AB and a number r between 0 and 180, there is exactly
one ray with endpoint A, extending on either side of AB, such
that the measure of the angle formed is r.
P
R
Postulate 2.11Angle Addition Postulate
If R is in the interior of PQS, then m PQR + m RQS = m PQS.
Q
Example 1: If m ABD = 44 and m ABC = 88, find m DBC.
S
Theorem 2.3Supplement Theorem
If two angles form a linear pair, then they are
supplementary angles.
A
D
B
C
Theorem 2.4Complement Theorem
If the noncommon sides of two adjacent angles
form a right angle, then the angles are complementary angles.
1
Example 2: If 1 and 2 form a linear pair and m 2 = 67, find m 1.
1
2
Statements
4
Reasons
Theorem 2.6
Angles supplementary to the same angle
or congruent angles are congruent.
Theorem 2.7
Angles complementary to the same angle
or congruent angles are congruent.
Theorem 2.8Vertical Angle Theorem
If two angles are vertical angles, then they are congruent.
Example 3: Given: 1 and 2 form a linear pair.
2 and 3 form a linear pair.
Prove: 1 = 3
Theorem 2.5Angle Congruence
Congruence of angles is reflexive, symmetric and transitive.
1
2
3
Example 4: If 1 and 2 are vertical angles and m 1 = x and m 2 = 228 ­ 3x, find m 1 and m 2.
2
QUIZ Review:p. 100
"Practice Quiz 2"
# 2 ­ 5
Theorem 2.9
Perpendicular lines intersect to form four right angles.
Theorem 2.10
All right angles are congruent.
Theorem 2.11
Perpendicular lines form congruent
adjacent angles.
Theorem 2.12
If two angles are congruent and
supplementary, then each angle is a right angle.
Theorem 2.13
If two congruent angles form a linear pair,
then they are right angles.
Find the measure of each numbered angle.
2. m 1 = 65 3. 6 and 8 are complementary and
m 8 = 47
Guided Practice:
1
2
6
7
8
1. Find the error. Thomas and Jacob wrote equations involving the angle measures shown. Who is correct? Why?
E
A
F
B
Thomas
Jacob
m ABE + m EBC
= m ABC
m ABE + m FBC
= m ABC
C
4. m 11 = x ­ 4
m 12 = 2x ­ 5
11
12
3
5. Given: 1 and 2 are supplementary
3 and 4 are supplementary
1 = 4
Prove: 2 = 3
1
2
3
Reasons
Statements
1. 1 and 2 are supplementary 1.
3 and 4 are supplementary
1 = 4
2. m 1 + m 2 = 180
m 3 + m 4 = 180
2. 3. m 1 + m 2 = m 3 + m 4 3.
4. m 1 = m 4
4.
4
Determine whether the following statements are always, sometimes or never true.
6. Two angles that are nonadjacent are ________ vertical.
7. Two angles that are congruent are _________ complementary to the same angle.
8. Two angles that form a linear pair are ___________ supplementary.
9. Two angles that form a linear pair are ____________
complementary.
10. Vertical angles are __________ right angles.
5. m 1 + m 2 = m 3 + m 4
5.
­ m 1 ­ m 4 6. m 2 = m 3
6.
7. 2 = 3 7.
Do you have any Vocab questions?
OBJECTIVES:
IN CLASS: p. 112 ­ 114
# 12 ­ 24, 27 ­ 32, 39 ­ 40, 44
HOMEWORK: p. 119
# 47 ­ 58
***Quiz next time over 2­7 & 2­8***
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