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Lesson 2-1 Inductive Reasoning and Conjecture
Lesson 2-2 Logic
Lesson 2-3 Conditional Statements
Lesson 2-4 Deductive Reasoning
Lesson 2-5 Postulates and Paragraph Proofs
Lesson 2-6 Algebraic Proof
Lesson 2-7 Proving Segment Relationships
Lesson 2-8 Proving Angle Relationships
Example 1 Angle Addition
Example 2 Supplementary Angles
OBJECTIVE: To write proofs involving
supplementary and complementary angles (2.9.8J)
(M8.D.1.1)
KEY CONCEPT:
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.
KEY CONCEPT:
POSTULATE 2.11
Angle Addition Postulate
• If R is in the interior of PQS, then
mPQR + mRQS = mPQS.
• If mPQR + mPQS, then R is in the
interior of PQS.
KEY CONCEPT:
THEOREMS
• 2.3 SUPPLEMENT THEOREM: If 2
angles for a linear pair, then they are
supplementary angles.
• 2.4 COMPLEMENT THEOREM: If the
noncommon sides of 2 adjacent angles
form a right angle, then the angles are
complementary angles.
TIME At 4 o’clock, the angle between the
hour and minute hands of a clock is 120º.
If the second hand stops where it bisects
the angle between the hour and minute
hands, what are the measures of the angles
between the minute and second hands and
between the second and hour hands?
If the second hand stops where the angle is bisected,
then the angle between the minute and second hands is
one-half the measure of the angle formed by the hour
and minute hands, or
.
By the Angle Addition Postulate, the sum of the two
angles is 120, so the angle between the second and hour
hands is also 60º.
Answer: They are both 60º by the definition of angle
bisector and the Angle Addition Postulate.
QUILTING The diagram below shows one square for
a particular quilt pattern. If
and
is a right angle, find
Answer: 50
If
and
form a linear pair and
find
Supplement Theorem
Subtraction Property
Answer: 14
If
and
find
.
Answer: 28
are complementary angles and
REVIEW
1. If 6 and 8 are complementary, 6,
7, and 8 for a straight line, and 8 =
47, what is the measure of 6 and 7?
6 = 43 and 7 = 90
2. If m11 = x – 4, m12 = 2x – 5, and 11
and 12 are supplementary, what is the
measure of 11 and 12?
11 = 59 and 12 = 121
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