SOLUTION: i just recently submitted this question"If an angle bisector of a triangle is the perpendicular bisector of the opposite side, then the triangle is isosceles" if someone can write

Algebra ->  Geometry-proofs -> SOLUTION: i just recently submitted this question"If an angle bisector of a triangle is the perpendicular bisector of the opposite side, then the triangle is isosceles" if someone can write       Log On


   

Question 267265: i just recently submitted this question"If an angle bisector of a triangle is the perpendicular bisector of the opposite side, then the triangle is isosceles" if someone can write it in indirect prove form not wether its true or false
Answer by Mr.Gardner(4) About Me  (Show Source):
You can put this solution on YOUR website!
Ok. Let triangle ABC be our triangle. Let ray BD bisect angle ABC and intersect segment AC at D such that segment AD is congruent to segment DC and angle BDC and angle BDA are right angles (The hypothesis)(It will help if you draw it out). We know that angle ABD and angle CBD are congruent because ray BD bisects angle ABC. We also know that angle ADB and angle CDB are congruent because they are both right. We ALSO know that side AD is congruent to side CD because ray BD bisects AC. Therefore triangle ADB and triangle CDB are congruent by AAS congruence and angle A is congruent to angle C. Therefore triangle ABC is isosceles because the the if the base angles of a triangle are congruent, then it is an isosceles triangle.