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Extensible Markup Language  |  1995-08-15  |  3KB  |  29 lines
  1. <?xml version="1.0" encoding="utf-8" ?>
  2. <!DOCTYPE card PUBLIC "-//Apple, Inc.//DTD card V 2.0//EN" "" >
  3. <card>
  4.     <id>41996</id>
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  11.     <content>
  12.         <layer>background</layer>
  13.         <id>25</id>
  14.         <text><span class="style10">athematics and its Applications (2 of 4)</span><span class="style7">Here </span><span class="style26">D, E</span><span class="style7"> and </span><span class="style26">F</span><span class="style7"> are the center-points of sides </span><span class="style26">AB</span><span class="style7">, </span><span class="style26">BC</span><span class="style7"> and </span><span class="style26">CA</span><span class="style7"> respectively. So, </span><span class="style26">DE</span><span class="style7"> is half the length of </span><span class="style26">AC</span><span class="style7">, </span><span class="style26">EF</span><span class="style7"> is half the length of </span><span class="style26">AB</span><span class="style7">, and </span><span class="style26">FD</span><span class="style7"> is half the length of </span><span class="style26">BC</span><span class="style7">. Thus, the shaded triangle, </span><span class="style26">DEF</span><span class="style7">, is </span><span class="style26">similar</span><span class="style7"> to the large triangle, and the angles at </span><span class="style26">D</span><span class="style7">, </span><span class="style26">E</span><span class="style7"> and </span><span class="style26">F</span><span class="style7"> are, respectively, equal to those at </span><span class="style26">C</span><span class="style7">, </span><span class="style26">A</span><span class="style7"> and </span><span class="style26">B</span><span class="style7">. Furthermore, the triangles </span><span class="style26">ADF</span><span class="style7">, </span><span class="style26">FEC</span><span class="style7">, </span><span class="style26">DBE</span><span class="style7"> and </span><span class="style26">EFD</span><span class="style7"> are all </span><span class="style26">congruent</span><span class="style7">, i.e. identical in shape and size, and are thus all similar to triangle </span><span class="style26">ABC</span><span class="style7">.A right-angled triangle is a triangle where one of the angles is 90 deg. </span><span class="style26">Pythagoras' theorem</span><span class="style7"> states that, in a right-angled triangle, the square of the length of the </span><span class="style26">hypotenuse</span><span class="style7"> (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides. So, in the triangle shown, below, </span><span class="style26">AC' = AB' + BC'</span><span class="style7">. Trigonometry relies on the recognition that in a right-angled triangle the ratio of the lengths of pairs of sides depends only on the sizes of the two acute angles (i.e. angles less than 90 deg) of the triangle.</span></text>
  15.     </content>
  16.     <content>
  17.         <layer>background</layer>
  18.         <id>23</id>
  19.         <text>ΓÇó ASTRONOMYΓÇó PHYSICSΓÇó CHEMISTRYΓÇó THE HISTORY OF SCIENCE</text>
  20.     </content>
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  23.         <id>36</id>
  24.         <text>4204060</text>
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