document.write( "Question 387958: Please help me with this problem. If a median is also an altitude of a triangle, prove the triangle is isosceles. \n" ); document.write( "

Algebra.Com's Answer #274257 by scott8148(6628) $\"\"$ $\"About$

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the strategy is:\r
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\n" ); document.write( "\n" ); document.write( "given ___ median and altitude\r
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\n" ); document.write( "\n" ); document.write( "median divides side into equal lengths\r
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\n" ); document.write( "\n" ); document.write( "altitude is perpendicular\r
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\n" ); document.write( "\n" ); document.write( "the median equals itself (reflection)\r
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\n" ); document.write( "\n" ); document.write( "the two right angles from the perpendicular are equal\r
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\n" ); document.write( "\n" ); document.write( "the two halves of the side divided by the median are equal (definition of median)\r
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\n" ); document.write( "\n" ); document.write( "so the two internal triangles are congruent by SAS\r
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\n" ); document.write( "\n" ); document.write( "the two sides of the larger triangle are congruent (CPCTC)\r
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\n" ); document.write( "\n" ); document.write( "the large triangle is isosceles by definition \n" ); document.write( "

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