document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193520>Question 193520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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. \r<BR>\n" );
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document.write( "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. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145254 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=145254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> # 1\r<BR>\n" );
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document.write( "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. \r<BR>\n" );
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document.write( "Note: Each endpoint only gets ONE other endpoint. Also, to form <i>any</i> polygon, you need AT LEAST three line segments.\r<BR>\n" );
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document.write( "So basic geometric shapes such as triangles, quadrilaterals, rectangles, squares, pentagons, hexagons, heptagons (7 sided polygon), octogons, etc... are examples of all polygons. \r<BR>\n" );
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document.write( "Equiangular Polygon: An <i>equiangular</i> 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.\r<BR>\n" );
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document.write( "Equilateral Polygon: An <i>equilateral</i> 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.\r<BR>\n" );
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document.write( "Regular Polygon: If a polygon is both equiangular AND equilateral, then it is then refered to as a <i>regular</i> 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).\r<BR>\n" );
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document.write( "To learn more about polygons, check out <a  rel=nofollow HREF=\"http://en.wikipedia.org/wiki/Polygon\">this page</a>\r<BR>\n" );
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document.write( "# 2\r<BR>\n" );
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document.write( "Let's say that we have the problem:\r<BR>\n" );
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document.write( "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? \r<BR>\n" );
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document.write( "A: \r<BR>\n" );
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document.write( "Let's first draw the picture that describes this problem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://i150.photobucket.com/albums/s91/jim_thompson5910/work/ladder.png\">\r<BR>\n" );
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document.write( "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\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "The Pythagorean Theorem: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where \"a\" and \"b\" are legs of the triangle and \"c\" is the hypotenuse\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the Pythagorean Theorem.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B7%5E2=25%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B7%5E2=25%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=x ALIGN=MIDDLE  ALT=\"a=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=7 ALIGN=MIDDLE  ALT=\"b=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=25 ALIGN=MIDDLE  ALT=\"c=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B49=625 ALIGN=MIDDLE  ALT=\"x%5E2%2B49=625\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 7 to get 49. Square 25 to get 625\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=625-49 ALIGN=MIDDLE  ALT=\"x%5E2=625-49\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 49 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=576 ALIGN=MIDDLE  ALT=\"x%5E2=576\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28576%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28576%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > 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.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=24 ALIGN=MIDDLE  ALT=\"x=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 576 to get 24. \r<BR>\n" );
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document.write( "So the solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=24 ALIGN=MIDDLE  ALT=\"x=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that the ladder reaches the 24 foot mark on the wall.  </SPAN>\n" );
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