Chapter 2 Geometry Measurement Section 2 2 Polygons

Chapter 2: Geometry & Measurement Section 2. 2: Polygons, Circles & Solids APPLIED MATHEMATICS, FOURTH EDITION, MATOVINA & YATES

Polygons “Poly” is from the Greek word “many, ” and the suffix “–gon” comes from the Greek word for “angled. ” Thus, a polygon is a flat figure with straight sides that has many angles. Keep in mind, in a polygon, the number of sides must be equal to the number of angles. That leads some people to define a polygon as a many-sided figure. NAME SIDES/ANGLES Triangle 3 Quadrilateral 4 Pentagon 5 PICTURE APPLIED MATHEMATICS, FOURTH EDITION, MATOVINA & YATES

Polygons - Continued NAME SIDES/ANGLES Hexagon 6 Octagon 8 Decagon 10 Dodecagon 12 PICTURE APPLIED MATHEMATICS, FOURTH EDITION, MATOVINA & YATES

Polygons - Example: Identify the following polygons. c. a. Hexagon Pentagon d. b. Octagon Oregon APPLIED MATHEMATICS, FOURTH EDITION, MATOVINA & YATES

Triangles The prefix tri- means three, so a triangle literally has three angles. TYPE PROPERTIES Equilateral All three angles are equal. Isosceles Exactly two angles are equal. Scalene No angles are equal. Right One angle is 90°. Acute All angles are less than 90°. Obtuse One angle is greater than 90°. Some triangles may fall into more than one of the categories but be sure treat each category according to its own properties. The sum of the interior angles of any triangle must be 180°. APPLIED MATHEMATICS, FOURTH EDITION, MATOVINA & YATES

Quadrilaterals The prefix quad- means four and lateral means side. Thus, a quadrilateral is a four-sided polygon. TYPE PROPERTIES Trapezoid Parallelogram Rectangle Rhombus Square Exactly one pair of opposite sides is parallel. Both pairs of opposite sides are parallel. All interior angles measure 90°. All sides are equal in length, and all angles measure 90°. Like triangles, quadrilaterals my fall into more than one category. For example, a square is also a rectangle. The sum of the interior angles is 360°. APPLIED MATHEMATICS, FOURTH EDITION, MATOVINA & YATES

Circles A circle is the set of all the points in a plane that are the same distance from a single point, called the center. The radius of a circle is the distance from its center to a point on the circle, and is indicated with the letter r. The diameter of a circle is the distance across a circle as measured through the circle's center and is indicated with the letter d. Note: d = 2 r. Instead of calling it the perimeter, the distance around a circle is called its circumference, and is indicated with the letter C. The ratio of the circumference to the diameter of a circle, C/d, is better known as π, which is approximately 3. 1415926…. APPLIED MATHEMATICS, FOURTH EDITION, MATOVINA & YATES

Solids A rectangular box has 6 faces (sides), 8 vertices (corners), and 12 edges. A pyramid has triangular sides that meet in an apex at the top and either a triangle or a rectangle (usually a square) at the base. A right circular cylinder has a rectangular side that is rolled into a tube so that it forms a circle on the top and bottom. APPLIED MATHEMATICS, FOURTH EDITION, MATOVINA & YATES