Two column proof

[VDAVISON]

In the figure below, we are given the following statements:
(a) m angle ACE = 58 degrees.
(b) AE is the perpendicular bisector of BC.
(c) BF is the bisector of ABG.
(d) GB is perpendicular to BE.

(The picture is that of a triangle with bisector down middle and also on the end is the angle GB with bisector BF)

Prove that m angle FBG = 74 degrees. (State all the statements that are necessary in your proof along with their reasons in a two-column table.)

 

[chivox]

Please read "Read Before Posting," which contains some very important instructions. If you are stuck somewhere, we need to see your work, so that we might help you better. On all of these homework problems, I would start with a picture. Look at what you've got, and get started with the solution process. If you can't get all the way to the end of the proof, post what you have, and you will find more experts here than you can shake a stick at. We'll be happy to help.

-Paul

 

[stapel]

In the figure below, we are given the following statements....

What "figure"...?

Eliz.

 

[VDAVISON]

Re:

In the figure below, we are given the following statements....

What "figure"...?

Eliz.

I could not put the picture in but it is a triangle with a bisector?

what I have so far on this one is:

Statement Reason
m angle ACE = 58 degrees given
m ABE = 58 degrees symmetric property
AE is the perpendicular given
Bisector of BC

 

[chivox]

You asked: Prove that m angle FBG = 74 degrees. (State all the statements that are necessary in your proof along with their reasons in a two-column table.)

74?? If GB is perpendicular to BE, don't you have mGBE = 90? Then, you already have in step 2 of your proof that ABE = 58. What's left (90 - 58) is 32, and if BF bisects ABG, wouldn't FBG be 16 (half that angle)? I don't understand where you're getting the complement of that angle from. I think a picture would be best. You can upload it directly to this board (read "Read Before Posting") by clicking the "Upload attachment" tab down below the editing window.

 

[VDAVISON]

You asked: Prove that m angle FBG = 74 degrees. (State all the statements that are necessary in your proof along with their reasons in a two-column table.)

74?? If GB is perpendicular to BE, don't you have mGBE = 90? Then, you already have in step 2 of your proof that ABE = 58. What's left (90 - 58) is 32, and if BF bisects ABG, wouldn't FBG be 16 (half that angle)? I don't understand where you're getting the complement of that angle from. I think a picture would be best. You can upload it directly to this board (read "Read Before Posting") by clicking the "Upload attachment" tab down below the editing window.

here is the picture for it, thanks

 

[chivox]

Now we see how pictures really help with geometry proofs. But look at what we've got. Your line segment for BG makes a 180-degree angle with mine, and we know mGBE (both of ours) is 90 degrees. It follows from this that mGBF = 74. Do you see it? Think parallel lines cut by a transversal.