Indirect proof written in two collumn format

Question

Given: Triangle ABC is not isosceles. Line segment BD is perpendicular to line segment AC.

Prove: Line segment BD is not a median (11 steps)

Answer 1

Courtney,

Try proving by starting out that it is and disproving that statement in the end.

If it is a median then...

AD=CD because we have assumed it's median

<BDA=<BDC because we have been told BD is perpendicular to AC

side BD is common to both triangles BDA AND BDC

∴Triangles BDA and BDC are congruent by the side-angle-side theorem

=> Sides BA and BC are equal because they are corresponding sides of two congruent triangles

But, we had started out saying that they are not equal (i.e. the triangle is not isosceles)

∴BD can not be a median

I hope this helps Courtney