Given BX bisects ?ABC Prove ?ABC is a right triangle

Question

Help me im really confused please im terrible at proofs 

 

Answer 1

The conclusion called for, "?ABC is a right triangle", does not follow from the hypothesis, "BX bisects ?ABC"; it matters not whether you speak of triangle ABC or angle ABC. 

 

As for a tip on writing proofs, think of them as essays.  You may be more familiar with the two-column format, but a proof is really just an essay.  It has a thesis (the statement to be proved), supporting sentences which may be arranged into one or more paragraphs, and a conclusion.  The statements used to support the conclusions you make are the definitions, postulates, and theorems you have studied. 

 

When writing a proof, take a look at the conclusion you are asked to justify, then survey all the definitions, theorems, and postulates that pertain to the object in question.  In this case, they should pertain to right triangles.  Are there any theorems that have the same conclusion as the one you are trying to draw?  Often, you will find one that fits quite readily, and the rest is just placing the definitions, postulates, and theorems into a logical sequence of statements that lead to the conclusion.  Take care to satisfy the hypotheses of any theorems or postulates you use.

 

I hope that proves helpful,

David