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Introduction to Angles and Triangles

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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