SOLUTION: How do i prove that given triangle ABC with the altitude from B of the same length as the altitude from C, then the triangle must be isosceles. I can prove this question without i

Question 52484: How do i prove that given triangle ABC with the altitude from B of the same length as the altitude from C, then the triangle must be isosceles.
I can prove this question without it saying altitude that is where i am confused.
thank you
Nadia
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
How do i prove that given triangle ABC with the altitude from B of the same length as the altitude from C, then the triangle must be isosceles.
I can prove this question without it saying altitude that is where i am confused.
altitude means perpendicular from a vertex to its opposite side..here we are
given
ABC is a triangle.
BE is altitude..means..E is on AC and BE is perpendicular to AC
CF ia altitude.........F is on AB and CF is perpendicular to AB
BE=CF
in triangles BEC and CFB,we have
BE=CF..given
angle BEC=90=ANGLE CFE...............given
BC=BC
so the 2 triangles are congruent.
EC=FB....similarly we can prove
EA=FA
adding
EC+EA = FB+FA
AC = AB...so ABC is isocelles triangle
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