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Angles and Polygons

Angles and Polygons. Sections 1.5 & 1.6. Notecard 16. Definition: Angle An angle is formed by two different rays with the same endpoint . The endpoint is the vertex of the angle. An angle is named using 1) three points, making sure the vertex is in middle

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Angles and Polygons

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  1. Angles and Polygons Sections 1.5 & 1.6

  2. Notecard 16 Definition: Angle An angle is formed bytwo different rays with the same endpoint. The endpoint is the vertex of the angle. An angle is named using 1) threepoints, making sure the vertex is in middle 2) just the vertexbut only when no other angle has the same vertex 3) a number assigned to the angle

  3. Notecard 17 Definitions: Angles Classified by measure: An acute angle has a measure between 0o and 90o A right angle has a measure of exactly 90o An obtuse angle has a measure between 90o and 180o A straight angle has a measure of 180o

  4. Notecard 18 Definition: Congruent Angles Two angle are congruent angles if they have the same measure. To show that two angles in a diagram are congruent, we put a matching arc inside each angle.

  5. Notecard 19 Definition: Angle Bisector: An angle bisector is a ray that divides an angle into two congruent angles.

  6. Notecard 20 Definitions: Complementary and Supplementary Angles Two angles are complementary angles if the sum of their measures is 90o. Two angles are supplementary angles if the sum of their measures is 180o.

  7. Notecard 21 Definition: Adjacent angles two angles that share a common vertex and side, but have no common interior points.

  8. Notecard 22 Definition: Linear Pair: Two adjacent angles whose sides form a straight line. The angles in a linear pair are always supplementary .

  9. Notecard 23 Definition: Vertical Angle Pairs: Vertical angles are formed when two lines intersect. The angle pairs only touch at the vertex. There are two pairs of vertical angles formed whenever two lines intersect.

  10. Notecard 24 Definition: measure of an angle To denote the measure of an angle, we write an “m” in front of the angle sign: o

  11. Notecard 25 Angle Addition Postulate: If P is in the interior of , then the measure of is equal to the sum of the measures of and . (Two measures of two adjacent angles can be added to represent the large angle they form.)

  12. Notecard 26 A polygon is a closed two-dimensional shape with straight(not curved) sides.

  13. Vocabulary A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon. A polygon that is not convex is called concave.

  14. Notecard 27 Definitions: Equilateral polygon- all sides are congruent. Equiangular polygon- all interior angles in the polygon are congruent. Regular polygon - a convex polygon that is both equilateral and equiangular.

  15. Notecard 28 Polygon Names 3 sides Triangle 4 sides Quadrilateral 5 sides Pentagon 6 sides Hexagon 7 sides Heptagon 8 sides Octagon 9 sides Nonagon 10 sides Decagon 11 sides Undecagon 12 sides Dodecagon n sides n-gon

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