Help

[Purple_Mango]

Hey guys,

I just started Specialist 1&2 about two weeks ago, and oh boy - I can definitely see myself burning out for this subject. So, anyway, the first topic for my school is Geometry and Proofs, and I seriously need some help for proofs. Most of the time, I'll end up staring at one question for half an hour before I give up and just move on to other work, because I don't know how to get from the information I start off with to the final answer/conclusion. HAH, what a great way to start this subject. So, any pointers on doing proofs? I'll really appreciate a response to this question!

In extension of the previous enquiry, can someone help me with this question revolving around similarity?
P is the point on side AB of ABC such that AP : AB = 1 : 3, and Q is the point on BC such that CQ : CB = 1 : 3. The line segments AQ and CP intersect at X. Prove that AX : AQ = 3 : 5.
So far for this question, I drew a diagram for it based on the information given (since it wasn't provided)... and I've also written ∠AXP = ∠CXQ (vertically opposite). That's about it. I could have written ∠AXC = ∠PXQ (vertically opposite), but I didn't really see a point, since I don't even know what I'm doing for this question.

Huge thanks in advance !! 

[RuiAce]

The purpose of doing this is to take advantage of similar triangles, which have a tendency of being subtle. Once \(QP\) is joined, the similar triangles become blatantly obvious.

Note, the deduction that \( BQ:BC = 2:3 \) follows from the fact that \( CQ:CB = 1:3 \), and similarly for \(BP:BA\).

____________________________________________________________________________


I leave the write-up as your exercise.


(I leave the generic tips to someone who actually did the VCE, because I'm not sure how they teach you guys this stuff.)

[Purple_Mango]

Thank you so much! Your response has been very helpful, as I can finally proceed further in my work! I'll at least be able to handle the write-up, so no worries there.

As soon as I read that line, I felt really dumb. Like what you said, it is blatantly obvious. Such a simple thing has opened up a very clear path. Looks like one piece of advice I can take is that I should think outside the box and add anything helpful to diagrams.