SOLUTION: I am working on Proportions and Similar Triangles. The practice question asks me to fill in proofs for the statements. The type of theorem I am working with is Side Splitter Theore

Question 1182374: I am working on Proportions and Similar Triangles. The practice question asks me to fill in proofs for the statements. The type of theorem I am working with is Side Splitter Theorem. For the additional practices, I would like to know how the proofs are given to the statement, I understand the algebraic equations related to the theorem, but I don't understand the definition that fits perfectly with the statement. Here is the practice assignment I attempted:
Given: △QXY with RS←→∥XY←→
Prove: XR/RQ=YS/SQ
Statements:
1.△QXY with RS←→∥XY←→
2.∠1=∠3,∠2≅∠4
3.△QXY∼△QRS
4.XQRQ=YQSQ
5.XQ=XR+RQ,YQ=YS+SQ
6.XR+RQ/RQ=YS+SQ/SQ
7.XR/RQ=YS/SQ
What are the proofs for the statements?
Answer by ikleyn(52817)   (Show Source): You can put this solution on YOUR website!
.

In this site, there is an entire textbook on Geometry, written by me.
See the link
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson

This link leads you to the list of topics.

Among these topics, there is a topic "Similar triangles".

Click on it.
You will see the list of lessons, related to this topic
    - Similar triangles
    - Similarity tests for triangles
    - Proofs of Similarity tests for triangles
    - In a triangle a straight line parallel to its side cuts off a similar triangle (**)
    - Problems on similar triangles (*)
    - Similarity tests for right-angled triangles
    - Problems on similarity for right-angled triangles
    - Problems on similarity for right-angled and acute triangles
    - One property of a median in a triangle
    - One property of a trapezoid
    - Miscellaneous problems on similar triangles (*)
    - Solved problems on similar triangles (*)

It is what the normal educated student should know regarding similarity of triangles.

Read it, and you will find there many facts and theories you should know.

If this list seems too long for you, I marked (*) the lessons you should look at first and foremost.

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