Download Geometry 1.6 ‐ Measuring Angles A. Angle (formed by two

Geometry
1.6 ‐ Measuring Angles
A. Angle (<) ‐ is formed by two rays that share a common endpoint
• The rays are the sides of the endpoint
• The endpoint is called the vertex of the angle
• When naming an angle, we either name only the vertex,
or name all three letters with the vertex named in the middle.
EXAMPLE: Name the angle below in as many ways as possible.
H
D
G
•
Congruent Angles ‐ two or more angles with the same measure
In other words, if m<1 = m<2 then we say that <1 < 2
• We do not say that m<1 m<2. The “m” stands for the word “measure” and when we talk about the measure of an angle we are talking about its value. Values are equal, objects are congruent. Sep 9­2:59 PM
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B. Classifying Angles. Write about the following types of angles and draw pictures of them on your notes.
Acute angle ‐ •
•
Obtuse angle ‐ •
Straight angle ‐ •
Right angle ‐ Sep 9­3:38 PM
2
C. Angle Addition Postulate: Similar to the segment addition, if point B is in the interior of angle AOC then m<AOB + m<BOC = m<AOC. Furthermore, if <AOC is a straight angle, then m<AOB + m<BOC = 180
A
B
O
B
C
A
O
C
1. Suppose m<1 = 42 and m<ABC = 88, use the angle addition postulate to find m<2.
A
1
B
2
C
Sep 9­3:40 PM
3
2. m<DAB = 740
A
3x
2x + 4
B
D
C
Sep 16­11:34 AM
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D. Identifying Angle Pairs
• Vertical Angles ‐ two angles whose sides are opposite rays
1
2
3
4
• Adjacent Angles ‐ to angles who share a common vertex and are beside each other
1
1
2
2
• Complementary Angles ‐ two angles whose measures have a sum of 90
350
2
1
550
• Supplementary Angles ‐ two angles whose measures have a sum of 180.
700
1100
1
2
Sep 9­3:45 PM
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E. Examples.
1. Name all pairs of angles in the picture that are (a) Vertical
1 2 3
6 54
(b) Supplementary
(c) Complementary
(d) Adjacent
Sep 9­3:47 PM
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F. Drawing Conclusions: Listed below are things you can conclude from a diagram and things you cannot conclude
Conclude: Adjacent angles
•
Adjacent supplementary angles
•
Vertical angles
•
Cannot Conclude:
Angles or segments are congruent
•
An angle is a right angle
•
Lines are parallel or perpendicular
•
Sep 9­3:47 PM
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Hon. Geom HW 1.6 p. 40 #s 1 ­ 8, 15 ­ 26, 35 ­ 37
Sep 16­11:42 AM
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