A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

In the figure below, ∠ABC ≅ ∠DEC and ∠GFE ≅ ∠DCE. Point C is the point of intersection between segment AG and segment BD, while point E is the point of intersection between segment AG and segment DF.

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Prove ΔABC ~ ΔGEF.

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1 Attachment
  3. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Here is the given figure. |dw:1440008861250:dw|

  4. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now let's add the given info.

  5. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1440008960006:dw|

  6. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you know how to prove triangles similar using only congruent angles?

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    AA triangle postulate?

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mathstudent55

  9. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Correct. Using vertical angles, we can do exactly that.

  10. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1440010430470:dw|

  11. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1440010452565:dw|

  12. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    By using the theorem: "Vertical angles are congruent." we can show that the vertical angles shown in the figure are congruent. Then we have two angles of one triangle congruent to two angles of the other triangle, and by AA Similarity, we prove the two triangles are similar.

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, right

  14. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    great

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    How would I put that into a paragraph proof?

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @mathstudent55

  17. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    By vertical angles, <DEC =~ to <FEG Since by given <ABC =~ DEC, then by transitive, <ABC =~ <FEG By vertical angles, <DCE =~ <BCA Since by given <GFE =~ <DCE, then by transitive, <BCA =~ <GFE By AA Similarity, ΔABC ~ ΔGEF

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you so much!

  19. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You're welcome.

  20. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.