Geometry: Prove: Angle APD is congruent to Angle BQE

[cyberspace]

I have a presentation for this geometry proof problem tomorrow and I wanted to make sure if I had made any mistakes.
Here's the diagram:

Given: Angle CPQ is congruent to Angle PQF
Prove: Angle APD is congruent to Angle BQE

Here are my statements and reasons:
1. Angle CPQ is congruent to angle PQF 1. Given
2. Angle CPQ is congruent to angle APD 2. Definition of Vertical Angles
3. Angle PQF is congruent to angle BQE 3. Definition of Vertical Angles
4. Angle APD is congruent to angle BQE 4. Transitivity and Symmetric Property

I'm not sure if my proof is right, because in my opinion, it seems too short. If this is wrong, can you please explain and show me what would be the right steps?
Thanks for your help in advance.

 

[sgtpepper]

Re: Geometry Proof Problem

I don't know all the names of the properties, but everything that you've said is true. However, I don't think this is the way you go about a proof. As you say, it seems short, but I haven't really done much work with proofs, so I wouldn't know. Maybe you should go a little deeper and say that angle CPQ is x, and angle APC is y. x and y add up to 180 degrees. Then APC and APD must add up to 180. APC is y, and so APD must be x. So CPQ and APD must be equal to each other. Which if you named it correctly, is the "definition of vertical angles". Again, I'm not too sure about proofs, but I hope I helped even a little.

 

[Loren]

Re: Geometry Proof Problem

Looks good to me. But I would suggest that unless the drawing was given, you should avoid making it look like those are right angles. In other words make the transversal on the bias rather than perpendicular to the parallel lines.

 

[cyberspace]

Re: Geometry Proof Problem

Yes, I made this picture. This is a word problem in which I had to draw out the diagram and show my proof.
But now that you metioned it, I think it's better to go with the transveral.
Thanks!
Is it also necessary for me to extend my steps?

 

[Deleted member 4993]

Re: Geometry Proof Problem

I do not believe you have complete problem statement.

You do not state that points {C,P,D} , {E,Q,F} and {A,P,Q,B} are collinear. Unless you state that - the claim of vertical angles do not hold good.