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Angles and Polygons

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Angles and Polygons

Sections 1.5 & 1.6

An angle consists of two different rays with the same endpoint.

The rays are the sides of the angle.

The endpoint is the vertex of the angle.

An acute angle has a measure between 0o and 90o

A right angle has a measure of 90o

An obtuse angle has a measure between 90o and 180o

A straight angle has a measure of 180o

Two angle are congruent angles if they have the same measure.

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

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

Two adjacent angles are a linear pair if their noncommon sides are opposite rays.

The angles in a linear pair are supplementary angles.

Two angles are vertical angles if their sides form two pairs of opposite rays.

Vertical angles are congruent to each other.

An angle is named with three points, just the vertex, or a number.

An angle can be named with just the vertex only if it is the only angle with that particular vertex.

The vertex is always the middle point when naming an angle with three points.

When naming an angle, always remember to put a symbol in front. Otherwise you are naming a point or plane.

To denote the measure of an angle, we write an “m” in front of the angle sign: o

If P is in the interior of , then the measure of is equal to the sum of the measures of and .

To show that two angles in a diagram are congruent, we put an arc inside each angle.

A polygon is a closed two-dimensional shape with straight sides.

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.

In an equilateral polygon, all sides are congruent.

In an equiangular polygon, all angles in the interior of the polygon are congruent.

A regular polygon is a convex polygon that is both equilateral and equiangular.

3 sidesTriangle

4 sidesQuadrilateral

5 sidesPentagon

6 sidesHexagon

7 sidesHeptagon

8 sidesOctagon

9 sidesNonagon

10 sidesDecagon

11 sidesUndecagon

12 sidesDodecagon

n sidesn-gon

- Complete the following sentences in your summary section for homework tonight:
- A vertical angle is different from a linear pair because …
- The similarities and differences of equilateral, equiangular, and regular are …