Question

BD is a median of the triangle ABC and ED is a perpendicular bisector of triangle ABC.

Is BDC isosceles? Prove it. DO NOT ASSUME THAT THE TRIANGLE IS RIGHT. YOU MUST PROVE IT USING ANGLES AND SIDES.

Answer 1

show ADE is congruent to triangle BDE

then use the fact that BD bisects AC

Answer 2

There is no such thing as a perpendicular bisector of a triangle.
Is ED the perpendicular bisector of AB?

Answer 3

My teacher wrote a triangle but I am assuming AB.

Answer 4

Ok. I just figured it out, and it's the same that phi wrote.
You can prove triangle AED is congruent to triangle BED.
That gives you AD is congruent to BD by CPCTC.
Then since BD bisects AC, AD is congruent to DC.
Then use transitive to prove what you need.

Answer 5

Okay. Thanks to you both!

Answer 6

wlcm

Answer 7

Now, I need to prove that ABC is right. I said that it is right because the median BD bisects the hypotenuse of the triangle and the length of BD is congruent to both AD and DC, or half of the hypotenuse.

I think there must be more but I am not sure. I feel like there is something to do with the perp. bisector but I am not sure what. I know that the perp. bisector made two congruent triangles, but other than that, I'm not sure about the rest of this proof.

Answer 8

triangle BED is a right triangle (given) label angle DBE = a and its other angle b
a+b=90 (the 3rd angle is 90)

now if you can show angle EAD is a and angle BCD is b, it follows that CBE must be 90

Answer 9

I understand this, however, is it like a theorem or something that the perpendicular bisector makes two congruent triangles? I know it is something like that for the altitude of right triangle to the hypotenuse, however, I do not know that much about the properties of perp. bisectors of triangles.