Module 7 answers math

Module 7: Geometry Goals After completing this module, you will be able to do the following:         Identify and name points, lines (parallel, intersecting, and perpendicular), segments, and rays. Name an angle three different ways. Classify angles and triangles. Identify complementary and supplementary angles and find the complement or supplement of a given angle. Find the measure of the third angle, given the measures of two angles in a triangle. Find the perimeter of a polygon. Find the circumference of a circle. Find the area and volume of several common geometric shapes. Overview Geometry evolved from rudimentary ideas of the ancient Egyptians who were concerned with the practical problems involving the measurement of areas and volumes. The Egyptians focused on the geometry that was needed to construct buildings and pyramids and did not care about mathematical derivations and proofs. This module also follows the same model. The word geometry is derived from the Greek words geo (earth) and metron (measure). Euclid, one of the most famous mathematicians wrote a collection of Greek mathematics titled The Elements. This book has dominated the teachings of geometry for the last 2000 years. The basic elements of geometry are points, lines, and planes. A point can be regarded as a location in space. A point has no breadth, no width, and no length. We represent a point as a dot and label it with capital letters such as A and B or Q and R. We can use points to make lines. Lines are combined in such a way as to make angles. In geometry, an angle is the figure formed by two sides with a common point called the vertex. For most practical purposes, we need to have a way of measuring angles. In this module, we study common methods to measure angles, as well as the distance around (perimeter), the area, and the volume of common geometric shapes and see how these apply to our common day lives. A point can be regarded as a location in space. A point has no breadth, no width, and no length. We can use points to make lines. A line is a set of points that extends infinitely in both directions. A line has no width or breadth, but it does have length. Lines are named with lowercase letters such as l, m, or n or by using two of the points on the line. In geometry, an angle is the figure formed by two rays (sides) with a common endpoint called the vertex. For most practical purposes, we need to have a way of measuring angles. The most common unit of measure for an angle is the degree. In general, the perimeter is the distance around an object. The perimeter of a polygon is the sum of the lengths of the sides. Note: In a regular polygon all sides are of equal length. The circumference C of a circle of radius r equals two times π times the diameter d. In the metric system the area of a square 1 centimeter on each side is 1 cm • 1 cm = 1 cm². Similarly, in the customary system we can define the area of a square 1 in. on each side as 1 in. • 1 in. = 1 in². To find the area of a figure, we must find the number of square units it contains. If we know the area of a rectangle, we can always find the area of a triangle. A rectangle is made up of two triangles. The volume of a rectangular solid is the number of unit cubes it takes to fill it. In the metric system a solid cube 1 centimeter on each side is defined to be the unit of volume, 1 cm • 1 cm • 1 cm = 1 cm³(read “one cubic centimeter”). Other units of volume are the cubic meter and, in the customary system, the cubic foot and cubic yard.