Median is an Altitude Problem

megacherrio

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Dec 22, 2014
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This is a hard problem I am struggling with a lot.
I have a triangle in which the median is drawn. I am given that the line bisects the main angle of the triangle and that it is a median.
I need to prove that it is isoceles and th median is an altitude.

I have tried a lot of things. I know all I have to get is that the two half's of the triangle are congruent because then I will know the two angles to the left and right of where the median intersects the base are right angles by the right angl theorem. However we sisnye learn pothagareum's theorm or anything. We know parallel lines, mostly isocoes triangles and quadrangles. I know parallel lines won't help and that we have to draw something in to figure it out.
I also know that it might be helpful yo prove the median is the perprendicular bisector

I just need help starting. What do I draw?? We can use any constructions that we could do with a compass
 
This is a hard problem I am struggling with a lot.
I have a triangle in which the median is drawn. I am given that the line bisects the main angle of the triangle and that it is a median.
I need to prove that it is isoceles and th median is an altitude.

I have tried a lot of things. I know all I have to get is that the two half's of the triangle are congruent because then I will know the two angles to the left and right of where the median intersects the base are right angles by the right angl theorem. However we sisnye learn pothagareum's theorm or anything. We know parallel lines, mostly isocoes triangles and quadrangles. I know parallel lines won't help and that we have to draw something in to figure it out.
I also know that it might be helpful yo prove the median is the perprendicular bisector

I just need help starting. What do I draw?? We can use any constructions that we could do with a compass

Sounds like maybe a case for the Law of Sines. You might find
http://2000clicks.com/mathhelp/GeometryLawOfSines.aspx
of help. Look under the SSA section.
 
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