Section 1.5 – Exploring Angle Pairs

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Transcript Section 1.5 – Exploring Angle Pairs

SECTION 1.5 – EXPLORING ANGLE
PAIRS
Students will be able to:
•
identify special angle pairs and use
their relationships to find angle
measures
Key Vocabulary
adjacent angles
complementary angles
linear pair
vertical angles
supplementary angles
angle bisector
SECTION 1.5 – EXPLORING ANGLE
PAIRS
Definition
Adjacent Angles:
2 coplanar angles with
a common side, a
common vertex, and
no common interior
points
Vertical angles:
2 angles whose sides
are opposite rays.
Example
Graphic
Section 1.5 – Exploring Angle Pairs
Definition
Example
Complementary angles:
2 angles whose
measures have a sum of
90. Each angle is called
the complement of each
other
< 3 𝑎𝑛𝑑 < 4
Supplementary angles:
2 angles whose
measures have a sum of
180. Each angle is called
the supplement of the
other
And
< 𝐵 𝑎𝑛𝑑 < 𝐶
Graphic
SECTION 1.5 – EXPLORING ANGLE
PAIRS
Problem 1:
Use the diagram at the right. Is the statement true?
Explain
a.
<AFE and <CFD are vertical angles.
b.
<BFC and <DFE are supplementary.
c.
<BFD and <AFB are adjacent angles.
Concept Check
• From an unmarked diagram, we can conclude if
angles are
• You cannot conclude from an unmarked diagram
SECTION 1.5 – EXPLORING ANGLE
PAIRS
Problem 2:
What can you conclude from the information in the
diagram?
SECTION 1.5 – EXPLORING ANGLE
PAIRS
Problem 2b:
Can you make each conclusion from the information
in the diagram? Explain.
a.
𝑇𝑊 is congruent to 𝑊𝑉
b.
<TWQ is a right angle
c.
𝑃𝑊is congruent to 𝑊𝑄
d.
𝑇𝑉 bisects 𝑃𝑄
SECTION 1.5 – EXPLORING ANGLE
PAIRS
A linear pair is a pair of adjacent angles whose noncommon
sides are opposite rays. The angles of a linear pair form
a _________________.
SECTION 1.5 – EXPLORING ANGLE
PAIRS
Problem 3:
<DEC and <FEC are a linear pair. What are the measures of
< 𝐷𝐸𝐶 𝑎𝑛𝑑 < 𝐹𝐸𝐶?
SECTION 1.5 – EXPLORING ANGLE
PAIRS
An angle bisector is a ray that divides an angle into
two congruent angles.
Its endpoint is a the _________________.
SECTION 1.5 – EXPLORING ANGLE
PAIRS
Problem 4:
𝐾𝑀 bisects < 𝐽𝐾𝐿. If m< 𝐽𝐾𝐿 = 72, what is m< 𝐽𝐾𝑀?
SECTION 1.5 – EXPLORING ANGLE
PAIRS
Lesson Check
SECTION 1.5 – EXPLORING ANGLE
PAIRS
Lesson Check