How Can You Solve the Homework Challenge on Vectors and Similar Triangles?

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SUMMARY

The discussion centers on solving a geometry homework problem involving vectors and similar triangles. The key point is that triangle OPQ is similar to triangle OSR due to the parallel lines PQ and SR, with Q being the midpoint of OR. This similarity allows for the conclusion that PQ is half the length of SR. The discussion emphasizes the importance of proper notation, specifically that PQRS should not be designated with the Δ symbol.

PREREQUISITES
  • Understanding of geometric principles, specifically similar triangles.
  • Knowledge of vector notation and properties.
  • Familiarity with midpoint theorem in geometry.
  • Basic skills in geometric proofs and justifications.
NEXT STEPS
  • Study the properties of similar triangles in-depth.
  • Learn about vector representation and operations in geometry.
  • Explore the midpoint theorem and its applications in geometric proofs.
  • Review proper notation and conventions in geometry to avoid common mistakes.
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Students studying geometry, educators teaching geometric concepts, and anyone looking to improve their understanding of vectors and triangle similarity.

LiHJ
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Homework Statement



Dear Mentors and PF Helpers,

Here's the question:

image.jpg


Homework Equations

The Attempt at a Solution



Here's my solutions:

Please let me know whether I'm right. Thank you

image.jpg

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Hi LiHJ. How would you justify saying PQ is half the length of SR?

Edit: the rest looks right, though you are a bit rough & ready with the geometry. PQRS shouldn't be designated using the Δ symbol! :)
 
Because the question mention that Q is the midpoint of OR and PQ is parallel to SR. So triangle OPQ is similar to triangle OSR. Therefore P is a midpoint of OS
 
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Thank you;)
 

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