document.write( "Question 970823: Show by means of angles that A=(-1,0), B=(4,6), and C=(10,1) are the vertices of an isosceles triangle. \n" ); document.write( "

Algebra.Com's Answer #593535 by Edwin McCravy(20055) $\"\"$ $\"About$

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Show by means of angles that A=(-1,0), B=(4,6), and C=(10,1) are the vertices of an isosceles triangle.
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document.write( "We draw the triangle to see which angles appear to be the base angles.\r\n" );
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document.write( "We would normally use distances to show that AB ≅ AC to show that ABC is\r\n" );
document.write( "isosceles. But we are instructed not to do it that way, but to show \r\n" );
document.write( "instead that ∠A ≅ ∠C.\r\n" );
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document.write( "First we find the slopes of all three sides:\r\n" );
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document.write( "Slope of AB:    \r\n" );
document.write( "Slope of AC:  \r\n" );
document.write( "Slope of BC:  \r\n" );
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document.write( "The base angles are acute angles so we use absolute value\r\n" );
document.write( "to insure that the tangent is positive:\r\n" );
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document.write( "Multiply top and bottom by 55\r\n" );
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document.write( "Now we do that for ∠C:\r\n" );
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document.write( "Multiply top and bottom by 66\r\n" );
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document.write( "So ∠A and ∠C have the same tangents and so they have the same measure\r\n" );
document.write( "and since the base angles of ΔABC are ≅, ΔABC is isosceles.\r\n" );
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document.write( "Edwin

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