SECTION 1.5 – EXPLORING ANGLE PAIRSStudents will be able to:• identify special angle pairs and use

their relationships to find angle measures

Key Vocabularyadjacent angles vertical angles

complementary angles supplementary angles

linear pair angle bisector

SECTION 1.5 – EXPLORING ANGLE PAIRS

Definition Example Graphic

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.

Section 1.5 – Exploring Angle Pairs

Definition Example Graphic

Complementary angles:

2 angles whose measures have a sum of 90. Each angle is called the complement of each other

Supplementary angles:

2 angles whose measures have a sum of 180. Each angle is called the supplement of the other

And

SECTION 1.5 – EXPLORING ANGLE PAIRSProblem 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 PAIRSProblem 2:

What can you conclude from the information in the diagram?

SECTION 1.5 – EXPLORING ANGLE PAIRSProblem 2b:

Can you make each conclusion from the information in the diagram? Explain.

a. TWQ is a right angle

b. bisects

SECTION 1.5 – EXPLORING ANGLE PAIRSA 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 PAIRSProblem 3:

<DEC and <FEC are a linear pair. What are the measures of

SECTION 1.5 – EXPLORING ANGLE PAIRSAn angle bisector is a ray that divides an angle into

two congruent angles.

Its endpoint is a the _________________.

SECTION 1.5 – EXPLORING ANGLE PAIRSProblem 4:

bisects If m = 72, what is m?

SECTION 1.5 – EXPLORING ANGLE PAIRSLesson Check

SECTION 1.5 – EXPLORING ANGLE PAIRSLesson Check