Answer & Explanation:Special instructions:1. Please follow all the directions under Strategy for success2. Please have in text references and citations in the answers3. Please have all answers in question answer formatPlease follow all directions. This is very important assignment!
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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. (Note that volume is measured in
cubic units.) As in the case of areas, the volume of a rectangular solid object equals the number of units
of volume it contains. The square root of a number a, denoted by √a, is one of the equal factors b of the
number a, that is, √a = b means that a = b². In any right triangle with legs of length a and b and
hypotenuse c, then a² + b² = c². Thus, if we are given the lengths of any two sides of a right triangle, we
can always find the length of the third side using the Pythagorean theorem. Note that the converse of the
theorem is also true.
Module 7: Geometry
Module 7: Assignment
Start by reading and following these instructions:
1. Quickly skim the questions or assignment below and the assignment rubric to help you focus.
2. Read the required chapter(s) of the textbook. Some answers may require you to do additional
research on the Internet or in other reference sources. Choose your sources carefully.
3. Consider the discussion and the any insights you gained from it.
4. Produce the Assignment submission in a single Microsoft Word or Open Office document. Be sure
to cite your sources, use APA style as required, check your spelling.
Assignment:
1. If the length of a ray is given by letter r and the length of a line is given by letter L, what
symbol would you use (=, <, >) to make the state true: r____L? Explain your reasoning.
2. A rectangle is 20 m by 10 meters. Discuss the different ways in which you can find the
perimeter. Which is the fastest?
3. Which is a better illustration of a circle: a perfectly round penny or a bicycle tire? Explain.
4. Squaring a number and finding the square root of a number are inverse operations. Can you
find two other inverse operations?
Strategy for success:
For question #1: You will give examples and reasoning for r=L, rL.
For question #2: How many ways can you find the perimeter? Please think of as many as you can.
For question #3: This is a creative question. We know that both penny and tire and circular in nature.
Therefore, the answer could be tricky. It would be interesting to see what you think.
For question #4: This is very straight forward. Generally, you will solve algebraic equations using
inverse operations. Just about every operation has an inverse. You should be able to pair them up and
find many examples.
Note: Please answer as required. Please CLEARLY label each question with answers showing all work.
Explain the logic by which you arrive at your answers. When applicable, show all steps of derivation.
…
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