Proving PS/PQ = TX/XR in ΔPQR with Parallel Lines

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In summary, the conversation discusses a geometry problem involving a given line parallel to one side of a triangle, and the intersection of that line with two other sides of the triangle. The goal is to prove that the ratio of two line segments in the triangle is equal to the ratio of two other line segments formed by the intersection of the given line and the sides of the triangle. The participants of the conversation are unable to solve the problem, but they suspect that the question itself may be incorrect.
  • #1
harimakenji
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Homework Statement


At ΔPQR, a line is drawn parallel to QR, cuts PQ at S and PR at T. Line SR and QT intersect at X. Show that PS / PQ = TX / XR


Homework Equations





The Attempt at a Solution


I can not achieve that proof. The best I can get is : PS / PQ = TX / XQ. Something wrong with me or the question?
 
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  • #2
I also got your result. I'm placing my bets on the faulty question :smile:
 
  • #3
Mentallic said:
I also got your result. I'm placing my bets on the faulty question :smile:

OK. Thanks a bunch !
 
  • #4
No worries. It's nice to see you actually know how to do this question, you have no idea how many high school students (even in year 12) getting nowhere in this kind of geometry.
 

FAQ: Proving PS/PQ = TX/XR in ΔPQR with Parallel Lines

What is the definition of similarity of triangles?

The similarity of triangles is a relationship between two triangles where their corresponding angles are equal and their corresponding sides are proportional.

How can the similarity of triangles be proven?

The similarity of triangles can be proven using the following methods: Angle-Angle (AA) similarity, Side-Angle-Side (SAS) similarity, and Side-Side-Side (SSS) similarity.

What are some real-life applications of similarity of triangles?

Similarity of triangles is used in various fields such as engineering, architecture, and surveying to determine the height, width, and distance of objects without directly measuring them. It is also used in computer graphics to create 3D models and in medical imaging to estimate the size and shape of internal organs.

How is the Pythagorean theorem related to similarity of triangles?

The Pythagorean theorem is used to determine the length of the third side of a right triangle when the lengths of the other two sides are known. This can be extended to similar triangles, where the ratio of the sides is the same, allowing us to find the missing side lengths of similar triangles.

Can all triangles be similar to each other?

No, not all triangles can be similar to each other. For two triangles to be similar, their corresponding angles must be congruent and their corresponding sides must be proportional. If the angles are not equal, the triangles are not similar. Additionally, if the sides are not proportional, the triangles are not similar.

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