Warm Up Match the angles that appear to be the same angle

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Warm UpMatch the angles that appear to be the
same angle
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Quiz Answers
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Angles and their Measures
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Angle Consists of two different rays that have
the same initial point. The rays are the sides
of the angle, and the initial point is the
vertex of the angle.
Sides BA BC Vertex
B
A
sides


vertex
C

B
NOTATION We say that this angle is named
, or , or .
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A point is in the interior of an angle if its
between points that lie on each side of the
angle. A point is in the exterior of an angle if
its not on the angle or in its interior.
Exterior
Interior
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Congruent Angles Angles that have the same
measure
? is congruent to
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How to Measure Angles
http//www.amblesideprimary.com/ambleweb/mentalmat
hs/protractor.html
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Acute Angles
(The measure of the angle is less than 90
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One way to remember acute angles. ACUTE When
you think of something that is cute, you might
think of babies or kittens.
These are all small, as are acute angles (less
then 90)
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Obtuse Angles
The measure of the angle is more than 90 and
less than 180
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One way to remember obtuse angles is. OBTUSE
sounds like OBESE When you think of obese,
you think of large things..
So a large angle is rather OBESE, or we classify
it as OBTUSE (greater then 90 and less then 180)
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Right Angles
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One way to remember Right Angles...
Right angles fall RIGHT between acute and obtuse
angles.
Right Angles
Acute Angles
Obtuse Angles
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Straight Angles
The measure of the angle is EXACTLY 180
180

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Adjacent Angles are two angles that share a
common vertex and side, but have no common
interior points.
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Angle Addition If P is in the interior of
, then
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More With Adjacent Angles

• If you know the measure of two adjacent angles,
  then you can solve for the larger angle that they
  create.

m BAC 65 and m CAD
24 So.. m BAD m BAC m CAD m
BAD 65 24 m BAD 89
B

C

A

D

• If you know the large angles measure, and one of
  the smaller anglethen solve for the existing
  angle.

m BAD 56 and m BAC
24 So.. m CAD m BAD m BAC m
CAD 56 - 24 m CAD 32
B

C

A

D
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Complementary Angles
When the sum of two angles equals 90 (think
complement with weight is smaller)
54 36 90
54
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Ex What is the Complement of 64 ?
90 -64 26
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Supplementary Angles
When the sum of two angles equals 180 (this is
when the tip about complement comes in handy)
52 128 180
52
128
Ex What is the Supplement of 117 ?
180 -117 63
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Important Terms!

• Point a spot in space that is represented by a
  dot

P

• Segment starts at one point and ends at another,
  this contains every point between

PM
P
M

• Ray begins at one point and goes endlessly in
  one direction

PM

• Line goes endlessly in both directions

PM
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Important Terms!

• Parallel Lines two lines that will never cross
• Perpendicular Lines two lines that form a right
  angle
• Intersecting lines two lines that cross
• Transversal A line that intersects two parallel
  lines

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Important Terms!

• Skew Lines lines in space that do not intersect
  and are not parallel. There are not in the same
  plane.
• Example AD and FE

C
B
A
D
E
G
F
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When you have two parallel lines intersected by a
transversal some cool things will
happenVertical angles congruent angles formed
by two intersecting lines.
Ex
Ex
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Corresponding Angles angles that correspond will
be congruent
Ex
Ex
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Alternate Interior the two angles inside of the
parallel lines and on opposite sides of the
transversal
Ex
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Alternate Exterior Two angles on the outside of
the parallel lines and on opposite sides of the
transversal
Ex
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Where to look for angles in the future

• Angle Bisectors
• Angle pair Relationships
• Proofs
• Perpendicular and Parallel lines (transversals)
• Triangles
• Similarity
• Trigonometry
• And Much More!!!!!