document.write( "Question 214194: Q.1: Find the lenghts of the sides of the triangle with vertices A(-4,0), B(3,4) and C(4,1).show that the triangle ABC is isosceles? \n" ); document.write( "

Algebra.Com's Answer #162103 by Edwin McCravy(20060) $\"\"$ $\"About$

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Q.1: Find the lengths of the sides of the triangle with vertices A(-4,0), B(3,4) and C(4,1).show that the triangle ABC is isosceles?\r
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document.write( "There are two ways. It will be instructive to learn\r\n" );
document.write( "both methods.\r\n" );
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document.write( "Find the length of AB by drawing this blue\r\n" );
document.write( "right triangle with AB as its hypotenuse: \r\n" );
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document.write( "The bottom leg of the blue triangle is obviously 7 units long.\r\n" );
document.write( "(The bottom leg looks purple since it's blue over a red x-axis).\r\n" );
document.write( "You can just count them. And the right leg of the blue triangle \r\n" );
document.write( "is obviously 4 units tall.  You can tell by looking at the units \r\n" );
document.write( "of the y axis.\r\n" );
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document.write( "Now AB is the hypotenuse of the blue right triangle. So we use\r\n" );
document.write( "the Pythagorean theorem:\r\n" );
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document.write( "Now we erase the blue right triangle and draw a\r\n" );
document.write( "green one:\r\n" );
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document.write( "We find the length of AC by drawing this green\r\n" );
document.write( "right triangle with AC as its hypotenuse:\r\n" );
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document.write( "The bottom leg of the green triangle is obviously 8 units long.\r\n" );
document.write( "And the right leg of the green triangle is obviously 1 unit tall.\r\n" );
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document.write( "Now AC is the hypotenuse of the green right triangle. So we use\r\n" );
document.write( "the Pythagorean theorem:\r\n" );
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document.write( "So the lengths of AB and AC are both equal to.\r\n" );
document.write( "Therefore triangle ABC is isosceles.\r\n" );
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document.write( "HERE'S THE SECOND WAY;\r\n" );
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document.write( "Use the distance formula to find AB:\r\n" );
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document.write( "Use the distance formula to find AC:\r\n" );
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document.write( "So the lengths of AB and AC are both equal to.\r\n" );
document.write( "Therefore triangle ABC is isosceles.\r\n" );
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document.write( "Edwin

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