Prove in two-column proof: The median to the base of an isosceles triangle is perpendicular to the base and bisects the angle opposite the base.

Answer 1

The median divides the isosceles triangle into 2 triangles

In those two triangles:

The median is a side common to both

There is a side of the isosceles triangle in each

The equally divided base is in each

Therefore the 2 triangles are congruent by SSS

The statements to be proved follow as corresponding parts of congruent triangles.

This is not written strictly as a 2 column proof...but you should be able EASILY to put into that format.