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C. N. Coln Geometry St. Barnabas HS Bronx, NY Rays and Angles Ch. 1.5 and 1.6

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A RAY consists of a point on a line and all points on one side of the point. K A D This ray can be called AK or AD The beginning of the name is the endpoint, A.

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Opposite rays are two rays of the same line with a common endpoint and no other points in common RAY CC TT A

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Oh, Mrs. C, you are tooooooo funny!

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This is an angle

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A n angle is a set of points that is the union of two rays having the same endpoint A n Side Vertex DD EE There are several ways to name this angle: A DAE EAD n

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In this case there is no confusion you name an angle by the vertex. A A

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obtuse angle acute angle

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A B C D How many angles do you see? A 1 B 2 C 3 D Huh?

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Degrees were developed by the Babylonians thousands of years ago. They divided a circle into 360 parts and called each part one degree.

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The symbol for degrees, as you probably already know, is a small superscript circle. 4537112

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This is an acute angle and it measures 61

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This is an obtuse angle and it measures 127

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A: 180B: 125C: 50D: 25

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Angles are congruent if they have the same measure. A B

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If point S is in the interior (middle) of angle PQR, then the measure of PQS + measure of SQR = measure of PQR P Q R S

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P Q R S The bisector of an angle is a ray whose endpoint is the vertex of the angle, and that divides the angle into two congruent angles. PQS = SQR ~

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Complementary angles are two angles that total 90 degrees 30 and ___ 27 and ___ 12 and ___ 63 60 78

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Supplementary angles are two angles that total 180 degrees 25 and ___ 67 and ___ 124 and ___ 155 56 113

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AngleComplementSupplement 28 49 67 100 147

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AngleComplementSupplement 2862 49 67 100 147

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AngleComplementSupplement 2862152 49 67 100 147

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AngleComplementSupplement 2862152 4941 67 100 147

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AngleComplementSupplement 2862152 4941131 67 100 147

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AngleComplementSupplement 2862152 4941131 6723 100 147

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AngleComplementSupplement 2862152 4941131 6723113 100 147

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AngleComplementSupplement 2862152 4941131 6723113 100none 147

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AngleComplementSupplement 2862152 4941131 6723113 100none80 147

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AngleComplementSupplement 2862152 4941131 6723113 100none80 147none

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AngleComplementSupplement 2862152 4941131 6723113 100none80 147none33

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Straight angle is an angle that is the union of opposite rays. It makes a straight line and measures 180

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Linear angles are two angles that share a side and make a line. We also called them supplementary angles Linear angles total 180

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Right angles are angles that measure 90

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Acute angles measure less than 90

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Obtuse angles are angles that measure more than 90 but less than 180

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Perpendicular lines are lines that intersect to form right angles. The shortest distance from any point to a line is the length of the perpendicular from the point to the line.

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A reflex angle is an angle that measures more than 180

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p. 18 # 3, 4 p. 21 #4-24 (e)