Question

Prove that AE,DC,BF bisect DEF

Answer 1

Should look something like that

Answer 2

how i see it on your image AE,CD and BF are bisector ,perpendicular on opposite side

yes ?

Answer 3

yes the right angle notation is there.

Answer 4

Yes, sorry I didn't reply at first

Answer 5

@Dahlioz

Would you clarify this question: AE,DC,BF bisect DEF?
Are you wanting to show that ray or segment AE bisects angle DEF?
Sorry, but I do not understand what it is you wish to show.

Answer 6

Yeah, that they all bisect the triangle DEF, excuse me for making it unclear.

Answer 7

@Directrix

Do you know how to do this?

Answer 8

I am not clear on what is given. I see that segment AE is marked to be perpendicular to segment BC but I do not see that segment AE bisects segment BC as @jhonyy9 mentioned.

Is it possible that you might post the theorem you wish to prove as it appears in your text? Thanks.

Answer 9

Unfortunately I was clumsy enough to lose the paper, so I did this from memory, if I recall correctly, what was given was only that the AE,CD,BF segments each had their origin in the vertices of the triangle, that they were all perpendicular to the opposite segments/sides, and that a second triangle; DEF is formed, with its vertices at the points where the AE,CD,BF segments meet the "opposite sides". What I whish to prove is that the AE,CD, and BF segments all bisect the DEF triangle.

Answer 10

The drawn triangle is only theoretical, wouldn't necessarily look exactly like this, I just felt it would be easier to have a visual image of it, but atleast the important properties were given, even though a bit unclear

Answer 11

Segments AE, BF, and CD are altitudes of triangle ABC. As such, all three intersect in a single point (point of concurrency called the orthocenter). Therefore, the given diagram is drawn incorrectly based on the given information.

Also, note that the orthocenter may fall inside, outside, or on the triangle.

See the attachment fro http://www.regentsprep.org/Regents/math/geometry/GC3/LConcurrence.htm

Answer 12

My conjecture is that the following is the correct given:

Segments AE, BF, and CD are perpendicular-bisectors of the sides of triangle ABC.

I do not know that to be true.

Answer 13

My mistake then. SO assuming the diagram was drawn correctly, the correct given is " Segments AE, BF, and CD are perpendicular-bisectors of the sides of triangle ABC", which is not true? Sorry, but I don't really understand this very well :/

Answer 14

We need the exact statement of the problem. When you find the paper on which the problem is given, then re-post the question.