# Similar Triangles Proof: ABC sim to RST, BX bisects angle ABC, SY bisects angle RST

#### jtayag0622

##### New member
Hi,
I am having a little bit of confusion with this two-column proof. I tried my very best to prove the two triangles are similar and I don't know if my answer is right. I have this feeling that aside from it's quite long, I also missed something or I totally messed it up. I don't know how to prove it using Triangle Angle-bisector Theorem or If it's even needed. I am not so sure. Please help ...

Here's the problem:

Here's what I've done

#### lev888

##### Junior Member
The angles on the right are equal. The angles at the top too since they are half of equal angles. The remaining angles are whatever remains from 180 and, therefore, are equal. So the triangles are similar. Seems like your proof is along the same lines but I couldn't follow.

#### jtayag0622

##### New member
The angles on the right are equal. The angles at the top too since they are half of equal angles. The remaining angles are whatever remains from 180 and, therefore, are equal. So the triangles are similar. Seems like your proof is along the same lines but I couldn't follow.
Yeah .. that's why I feel like my proof is wrong. just can't think of how to shorten it. I guess there's a way to prove the two triangles are similar using two-column proof and is shorter and easier to follow. oh gosh . why even bother to prove it hehe . kidding ...

#### lev888

##### Junior Member
You don't think what I wrote is a short proof?

#### Dr.Peterson

##### Elite Member
Yeah .. that's why I feel like my proof is wrong. just can't think of how to shorten it. I guess there's a way to prove the two triangles are similar using two-column proof and is shorter and easier to follow. oh gosh . why even bother to prove it hehe . kidding ...
Your proof is fine, and can't be significantly shortened within the constraints of the style you are following.

The way to shorten it is either to change to paragraph format (like lev888's summary), or to tighten up some of the details of the algebra by not having to state a property for each step. Your format is inherently long, because it breaks apart every step. When mathematicians write proofs, they trust that the reader can fill in simple details without having everything spelled out for them; the two-column format forces you to take small steps, which can be good for learning (though I think it may take students' attention away from the big ideas of proof).

Don't worry about making compact proofs. That's not your goal right now.

#### jtayag0622

##### New member
Your proof is fine, and can't be significantly shortened within the constraints of the style you are following.

The way to shorten it is either to change to paragraph format (like lev888's summary), or to tighten up some of the details of the algebra by not having to state a property for each step. Your format is inherently long, because it breaks apart every step. When mathematicians write proofs, they trust that the reader can fill in simple details without having everything spelled out for them; the two-column format forces you to take small steps, which can be good for learning (though I think it may take students' attention away from the big ideas of proof).

Don't worry about making compact proofs. That's not your goal right now.
Thanks! I wanna learn Math so well and fast, but I don't know why and how my brain processes Math information that it always messes up.

#### Jomo

##### Elite Member
Thanks! I wanna learn Math so well and fast, but I don't know why and how my brain processes Math information that it always messes up.
It is a good idea to learn math well! As far as learning it fast, that is my concern. Before moving on in math you must learn the previous material perfectly. That is what is important! Now some people can learn the material well and very fast while others can learn it very well but at a slower pace. My advice is not to go quicker than you can really handle!

#### jtayag0622

##### New member
It is a good idea to learn math well! As far as learning it fast, that is my concern. Before moving on in math you must learn the previous material perfectly. That is what is important! Now some people can learn the material well and very fast while others can learn it very well but at a slower pace. My advice is not to go quicker than you can really handle!
so true! Thank you . Well, I will start learning Precalculus next year. Hope this forum can help me verify answers. Thanks again!

#### Jomo

##### Elite Member
so true! Thank you . Well, I will start learning Precalculus next year. Hope this forum can help me verify answers. Thanks again!
Good luck and go at a reasonable pace for you. Anytime you need help stop by the forum!