Degrees: Measuring Angles We measure the size of an angle using
degrees. Example: Here are some examples of angles and their degree
measurements.
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Acute Angles An acute angle is an angle measuring between 0 and
90 degrees. Example:
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Obtuse Angles An obtuse angle is an angle measuring between 90
and 180 degrees. Example:
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Straight Angle A right angle is an angle measuring 180 degrees.
Examples:
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Supplementary Angles Two angles are called supplementary angles
if the sum of their degree measurements equals 180 degrees.
Example: These two angles are supplementary.
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These two angles can be "pasted" together to form a straight
line!
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Complementary Angles Two angles are called complementary angles
if the sum of their degree measurements equals 90 degrees. Example:
These two angles are complementary.
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These two angles can be "pasted" together to form a right
angle!
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Review State whether the following are acute, right, or obtuse.
1. 2. 3. 4. 5. ? ? acute obtuse right obtuse acute
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Complementary and Supplementary 1. Two angles are
complementary. One measures 65 degrees. 2. Two angles are
supplementary. One measures 140 degrees. Find the missing angle.
Answer : 25 Answer : 40
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Complementary and Supplementary Find the missing angle. You do
not have a protractor. Use the clues in the pictures. 1. 2. x 55165
x X=35 X=15
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1. 9 0 x y z x = y = z = 2. 11 0 x yz x = y = z =
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Vertical Angles are angles on each side of intersecting lines 9
0 x y z 1.90 and y are vertical angles x and z are vertical angles
11 0 x yz 2. 9 0 11 0 70 11070 The vertical angles in this case are
equal, will this always be true? 110 and y are vertical angles x
and z are vertical angles Vertical angles are always equal
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Vertical Angles Find the missing angle. Use the clues in the
pictures. 58 xX=58
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Can you find the missing angles? 20 C J D E F G H 70 90 70 20
90
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Can you find these missing angles 52 B A FE D C 60 G 68
6052
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Triangles Can be classified by the angle measures
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Acute Triangle Has three acute angles (less than 90
degrees)
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Obtuse Triangle Triangle with one obtuse angle (greater than 90
degrees)
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Right Triangle Has one right angle (90 degree)
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Triangles Can be classified by the number of congruent
sides
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Scalene Triangle Has no congruent sides (all angles, and sides
are different)
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Isosceles Triangle Has at least two congruent sides
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Equilateral Triangle All three sides are congruent
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Equiangular Triangle Triangle with 3 equal angles Which can
only happen in a equalateral triangle
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Triangles Cut any shape triangle out of a sheet of paper. Tear
off the corners. Piece them together by having the corners touch.
The corners form what type of angle?
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Triangles The sum of the angles of a triangle is 180
degrees
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Equiangular Triangle Triangle with 3 equal angles If all the
angles must add to 180 and be the same.. Then, x+x+x = 180 3x = 180
X = 60
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Triangles If you know 2 angles, then you can always figure out
the 3 rd
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31 Triangle Inequalities
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32 Triangle Inequality Theorem: The sum of two smaller sides of
a triangle must be greater than the length of the largest side. a +
b > c a + c > b b + c > a Example:Determine if it is
possible to draw a triangle with side measures 12, 11, and 17. 12 +
11 > 17 Yes 11 + 17 > 12 Yes 12 + 17 > 11 Yes Therefore a
triangle can be drawn.
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33 Angle Side Relationship The longest side is across from the
largest angle. The shortest side is across from the smallest angle.
AB = 4.3 cm BC = 3.2 cm AC = 5.3 cm 54 37 89 B C A
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34 Triangle Inequality examples For the triangle, list the
angles in order from least to greatest measure. C A B 4 cm 6 cm 5
cm
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Triangles
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Congruent Triangles
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Two geometric figures with exactly the same size and shape. The
Idea of a Congruence A C B DE F
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Congruent Triangles Have congruent corresponding parts, sides
and angles May be flipped and/or rotated BE CAREFUL WHEN YOU NAME
THE SHAPE
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Congruent Triangles are named such that the corresponding
angles are in the same order
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Write the congruence statement A B C D E F
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Name the congruent triangles List the congruent sides and
angles Angles Sides