curve—continuous set of points (includes lines)

simple curves—do not intersect themselves

closed curves—start and end at same point

simple closed simple, not closed simple closed closed, not simple

A polygon is a simple closed plane figure made up of line segments. Polygon

A convex polygon is a polygon in which all interior angles have measures less than 180°. Convex Polygon

A concave polygon is a polygon in which at least one interior angle has a measure greater than 180°. Concave Polygon

Types of Polygons convex concave

side—segment making up part of a polygon

vertex—corner of a polygon; where two sides meet

Number of Sides Name quadrilateral triangle pentagon hexagon heptagon

Number of Sides Name nonagon octagon decagon dodecagon n-gon n n

regular polygon—all sides same length, all angles same measure

Example 1 Name each polygon and indicate whether it is regular. ABCD is a quadrilateral. DD AABB CC

Name each polygon and indicate whether it is regular. EFGHIJ is a regular hexagon. JJ EE GG HH II FF Example 1

scalene triangle: A triangle with no two sides equal in length.

isosceles triangle: A triangle with at least two sides equal in length.

equilateral triangle: A triangle with all sides equal in length.

acute triangle: three acute angles 60° 75° 45°

right triangle: one right angle 50° 40°

obtuse triangle: one obtuse angle 20° 30° 130°

Classify each triangle according to the measures of its angles and the lengths of its sides. Example 2

BB AA CC ABC is obtuse scalene.

EE DDFF DEF is right isosceles.

HH GGII GHI is acute equilateral.

Theorem In any triangle, the sum of the measures of the angles is 180°: in ABC m A + m B + m C = 180°.

Write and solve an equation to find m X. XX YYZZ ?? 116° 22° Example 3

m X + m Y + m Z = 180 m X = 180 m X = 180 m X = 42° Example 3

A quadrilateral is a four-sided polygon. Quadrilateral

A trapezoid is a quadrilateral with at least one pair of parallel sides. Trapezoid

A parallelogram is a quadrilateral with two pairs of parallel sides. Parallelogram

A rectangle is a parallelogram with four right angles. Rectangle

A rhombus is a parallelogram with four congruent sides. Rhombus

A square is a rectangle with four congruent sides. Square

A diagonal is a line segment joining any two nonadjacent vertices of a polygon. Diagonal

number of diagonals from one vertex number of sides, n number of triangles formed Triangle sum of angle measures °

number of diagonals from one vertex number of sides, n number of triangles formed Quadrilateral sum of angle measures (180) = 360°

number of diagonals from one vertex number of sides, n number of triangles formed Pentagon sum of angle measures (180) = 540°

number of diagonals from one vertex number of sides, n number of triangles formed Hexagon sum of angle measures (180) = 720°

Find the sum of the measures of the angles in a regular octagon. 6(180) = 1,080° Example 4

Find the measure of each angle in a regular octagon. = 135° 1,080 8 Example 4

Write and solve an equation to find m A. BB AA CC 120° 55° DD 80° Example 5

m A = 360 m A = 360 m A = 105° m A – 255 = 360 – 255 Example 5