Question 193520: 1. What is a polygon? What is the difference between an equiangular polygon, an equilateral polygon, and a regular polygon? Provide an example of each.
2. We can use the Pythagorean theorem to solve problems that involve right triangles. Provide an example of a day-to-day situation that involves right triangles and the use of the theorem.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! # 1
A polygon is simply a series of line segments connected in such a way that EVERY endpoint of EVERY line segment connects to some endpoint of another line segment.
Note: Each endpoint only gets ONE other endpoint. Also, to form any polygon, you need AT LEAST three line segments.
So basic geometric shapes such as triangles, quadrilaterals, rectangles, squares, pentagons, hexagons, heptagons (7 sided polygon), octogons, etc... are examples of all polygons.
Equiangular Polygon: An equiangular polygon is a polygon that has all angles equal to one another. For example, a rectangle is an equiangular polygon since all of its angles are equal to 90 degrees. Note: an equiangular polygon does NOT make the polygon an equilateral polygon.
Equilateral Polygon: An equilateral polygon is a polygon that has all equal sides. By definition, a square is an equilateral polygon since all of its sides are equal to one another. Note: if a polygon is an equilateral polygon, it does NOT also mean that it is an equiangular polygon.
Regular Polygon: If a polygon is both equiangular AND equilateral, then it is then refered to as a regular polygon. A regular polygon then has all angles that are equal to one another and all side lengths that are equal to one another. An equilateral triangle is in fact a regular polygon since all three of its angles are equal to one another (which means that it is both equiangular and equilateral).
To learn more about polygons, check out this page
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# 2
Let's say that we have the problem:
Q: A 25 foot ladder is leaning against a wall. The base of the ladder is 7 feet from the base of the wall. How high up the wall does the top of the ladder reach?
A:
Let's first draw the picture that describes this problem:
Take note that the wall is assumed to form a right angle with the ground. If it wasn't, we couldn't use the Pythagorean Theorem
From the drawing, we can see that we have a triangle with legs of "x" and 7 feet along with a hypotenuse of 25 feet. The goal now is to solve for "x". To do so, we need the Pythagorean Theorem.
The Pythagorean Theorem:  where "a" and "b" are legs of the triangle and "c" is the hypotenuse
Start with the Pythagorean Theorem.
 Plug in  ,  and 
 Square 7 to get 49. Square 25 to get 625
 Subtract 49 from both sides.
 Combine like terms.
 Take the square root of both sides. Note: we're only going to worry about the positive square root since a negative length doesn't make sense.
 Take the square root of 576 to get 24.
So the solution is which means that the ladder reaches the 24 foot mark on the wall.
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