SOLUTION: If two altitudes of a triangle are equal , prove that the triangle is an isosceles triangle .

Question 206813: If two altitudes of a triangle are equal , prove that the triangle is an isosceles triangle .
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
altitudes are the same,,,,,,,,,,,,,,,given
.
Altitudes are perpendicular to a side,
therefore resultant triangles are rt triangles,,,,,,,,def altitude & def rt triangle
.
{ 2 sketches might help, isosceles triangles with altitudes to each equal side)
.
Base of the triangles are equal, ,,,,,,,,,,,same side
.
Triangles created by altitudes and common base
are congruent,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,by HL( hypotenuse leg)
.
Therefore, side of each triangle, bisected by the altitude
are equal, and base angles are equal,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,by CPCTC
.
Therefore, triangles are isosceles,,,,,,,,,,by def of isosceles triangle
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(2 angles equal)
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