Download 1.4 Angles and Their Measures

1- 4
Angles
A) Terms
• 1) Angle – consists of 2 different rays that have the
same endpoint.
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a) rays are called the sides
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b) the endpoint is called the vertex
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c) angles are measured in degrees using a
protractor.
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d) symbol for angle: “<“
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e) measure <B denote: m<B or
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measure <ABC denote: m<ABC
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f) congruent angles are angles that have the
same measure.
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denote: <ABC  <DEF
C) Other Terms:
• 1) A point is in the interior of an angle it it is
between the 2 rays or inside the angle.
• 2) A point is in the exterior of an angle if it lies
outside the angle.
•
Ex.
•
exterior
interior
exterior
• 3) Classify Angles:
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a) Acute Angle - measures less than 90°.
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b) Right Angle – measures 90°
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c) Obtuse Angle – measures between
90° and 180°.
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d) Straight Angle – measures 180°
• Ex. Label the Angles below.
• 1)
2)
3)
• 4)
• 4) Two angles are Adjacent angles if they
share a common vertex and side, but have no
common interior points.
• Ex.
•
A
C
•
B
D

• <ABC is adjacent to <CBD
5) Angle Bisector
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- is a ray that divides the angle in half
• Ex. Find x. BC bisects <ABD. <ABC = x + 3
and <CBD = 3x – 1.
B) Postulates
• 1) Postulate 3: Protractor Postulate
• - The measure of angles are from 0° to 180°.
• 2) Postulate 4: Angle Addition Postulate
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If P is in the interior of <RST, then
m<RSP + m<PST = m<RST
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• Ex.
R  m<RSP

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P
m<RST


•
S
m<PST
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T