A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

last question of the night... promise

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

    In square $ABCD$, $E$ is the midpoint of $\overline{BC}$, and $F$ is the midpoint of $\overline{CD}$. Let $G$ be the intersection of $\overline{AE}$ and $\overline{BF}$. Prove that $DG = AB$.

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

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

    all i know is that BF = AE and BCF and ABE are congruent

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

    i also cannot decide if BG is perpendicular to AE... or not?

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

    well this is a pretty simple question if ur using co-ordinate geometry. :) |dw:1440261844607:dw|

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

    the equation of a line passing through points A(a,b) and B(m,n) can be written as - \[\frac{ y-b }{n-b}=\frac{ x-a }{ m-a }\]

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

    is there a way to solve it using properties of quadrilaterals and triangles, because thats what we're working on in class right now...

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

    ok lemme think that way :)

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

    we can use trigo right?

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

    we havent gotten to trigo yet...

  11. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    4 angles of a quad add to 360

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

    sorry, how do we know that angle BEA is 60 degrees?

  13. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    scratch that, thats not 60, lets start over

  14. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1440263391261:dw|

  15. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    so your earlier observation still holds : `BG is perpendicular to AE... `

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

    @ganeshie8 where do i go from there? I can make a series of expressions for each angle..but would that really help?

  17. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Here is the complete proof : 1) From the below diagram, clearly, \(DH\perp AG\) and \(BG\perp AE\). 2) \(\triangle ABG \sim \triangle AOH\) by \(AA\) similarity, so \(\dfrac{AO}{OG}=\dfrac{AH}{HB}\implies AO=OG\) 3) \(\triangle ODG\cong \triangle ODA\) by \(SAS\) congruence 4) \(DG\cong DA\) by CPCTC. |dw:1440268645673:dw|

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

    Thanks so much @ganshie!

  19. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    np

  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.