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Teacher Notes
Exploring Angles
Objective: To identify angles and classify angles, to use the Angle Addition Postulate to find the
measures of angles, and to identify and use congruent angles and the bisector of an angle.
Definitions:
 Angle-two rays that form an angle
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Ray-has exactly one endpoint and that point is always named first
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Opposite rays-Two rays that share a common endpoint.
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Sides-Two rays make up the sides of the angle
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Vertex-The common endpoint of two rays
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Interior-Location of points that lie on a segment of the angle
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Exterior-Location of points that lie outside of the interior of the angle
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Degrees-A unit used to measure angles
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Congruent angles-Angles that have the same measure
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m<ABC-Is read “the measure of angle ABC”
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Right angle-<A is a right angle if m<A is 90
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Acute angle-<A is an acute angle if m<A is less than 90
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Obtuse angle-<A is an obtuse angle if m<A is greater than 90 but less than 180
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Straight angle-<A is a straight angle if m<A is 180
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Angle bisector-Divides an angle into two congruent angles
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Protractor-Tool used to measure angles in degrees
Notes:
 Naming Angles-Angles are named with three letters; the endpoint, the vertex, then the other
endpoint. The vertex letter is always the one named in the middle.
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Using a protractor-To find the measure of an angle using a protractor, place the center point of
the protractor over the vertex of the angle. Then align the mark labeled 0 on either side of the
scale with one side of the angle.
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Angle Addition Postulate- If R is in the interior of <PQS, them m<PQR + m<RQS = m<PQS. If
m<PQR + m<RQS = m<PQS, then R is in the interior of <PQS.
1. Example:

List three rays make up the sides of these angles?
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What is the vertex of this angle?

List at least six angles present in this figure.
QP,QR,QS
po int Q
PQR, RQS , SQR , TQR , PQS , TQS
S
Q
R
T
P
2. Example:
 Using the above picture, identify each type of angle.
PQR -acute
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
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PQT -right
TQS -straight
RQT -obtuse
3. Example:
 Find the measure of each angle based on the information given.
 If mTQP is 90 and mPQR is 55, what is mTQR ? 145
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If mTQP is 90 and mPQR is 34, what is mTQR ? 124
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If mTQP is 90 and mPQR is 62, what is mTQR ? 152

If
QR is the angle bisector of PQS , what is mSQR ? 45