Angles and PolygonsSections 1.5 & 1.6

Notecard 16Definition: AngleAn 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 middle2) just the vertex but only when no other angle has the same vertex3) a number assigned to the angle

Notecard 17Definitions: 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

Notecard 18Definition: Congruent AnglesTwo 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.

Notecard 19Definition: Angle Bisector:

An angle bisector is a ray that divides an angle into two congruent angles.

Notecard 20Definitions: 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.

Notecard 21Definition: Adjacent angles

two angles that share a common vertex and side, but have no common interior points.

Notecard 22Definition: Linear Pair: Two adjacent angles whose sides form a straight line.

The angles in a linear pair are always supplementary .

Notecard 23Definition: 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.

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

Notecard 25Angle 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.)

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

Notecard 27A 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.

Notecard 28Definitions: 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.

Notecard 29 Polygon Names

3 sides Triangle4 sides Quadrilateral5 sides Pentagon6 sides Hexagon7 sides Heptagon8 sides Octagon9 sides Nonagon10 sides Decagon11 sides Undecagon12 sides Dodecagonn sides n-gon