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anonymous

  • one year ago

Determine if the two figures are congruent and explain your answer.

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  1. anonymous
    • one year ago
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  2. anonymous
    • one year ago
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    I know they ARE congruent I just need help explaining why.

  3. anonymous
    • one year ago
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    @ganeshie8 @Elsa213 @poopsiedoodle @mathmath333 @OregonDuck @Keigh2015 @Jaynator495 @work12345 @wampominater @ROSEQUEEN2014 @uybuyvf @undeadknight26

  4. anonymous
    • one year ago
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    @phi

  5. anonymous
    • one year ago
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    @phi Please help

  6. phi
    • one year ago
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    if you divide each figure into two triangles and show each triangle is congruent by side-side-side, to the corresponding triangle in the other figure, that would prove the figures are congruent.

  7. anonymous
    • one year ago
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    That is what I say in my own words or do I have to do it too??

  8. phi
    • one year ago
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    that is how to show the figures are congruent. but then you have to do the work. the length of each side can be found using the distance formula. do you know how to do that ?

  9. anonymous
    • one year ago
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    d= sqrt(x_2-x_1/y_2-y_1)?

  10. anonymous
    • one year ago
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    I totally forgot but I know it is something like that

  11. phi
    • one year ago
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    the idea is based on the pythagorean theorem a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

  12. phi
    • one year ago
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    the formula tells you how to find the length of each side using the coordinates but in your graph, we can just count.

  13. phi
    • one year ago
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    For example the leg from point A to point D |dw:1438103882199:dw|

  14. anonymous
    • one year ago
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    ye but how do we do it on mines?

  15. phi
    • one year ago
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    it looks like if we slide the figure to try to overlay the other figure, side AD matches up with the side GH so find the length of GH. if you get sqrt(17) then they are the same length

  16. phi
    • one year ago
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    make a triangle using side GH it has height 1 and width 4

  17. anonymous
    • one year ago
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    |dw:1438104168143:dw|

  18. anonymous
    • one year ago
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    Now what?

  19. phi
    • one year ago
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    yes. now pick another side in the first figure. side CD and compare it to side EH in the other figure.

  20. anonymous
    • one year ago
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    In the problem or example?

  21. phi
    • one year ago
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    The examples are from your problem. In other words, we have already shown AD and GH have the same size. now we do CD and EH

  22. anonymous
    • one year ago
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    CD= Length 1; Width 4 EH= Length -4; Width 1 Am I right?

  23. phi
    • one year ago
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    yes, but we don't care if it's -4. when we find the length -4*-4 = 16 (always positive) so if they have the same numbers 1 and 4 then the lengths will end up being the same

  24. anonymous
    • one year ago
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    CD 1*1 + 4*4 = 16+1 = 17 = sqrt17 EH 1*1 +-4*-4 = 16 +1 = 17 = sqrt17 So segment CD and EH are congruent.

  25. phi
    • one year ago
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    yes

  26. anonymous
    • one year ago
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    So now what do I do?

  27. phi
    • one year ago
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    I would do BC and FE (I mentally shifted the figures so they lay on top of each other to decide which legs should match up)

  28. anonymous
    • one year ago
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    BC: Height 2; Width -1 FE: Height 1; Width 2 Right?

  29. phi
    • one year ago
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    yes

  30. anonymous
    • one year ago
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    BC 2*2 + -1*-1 = 2+1 = 3 = sqrt3 FE 1*1 + 2*2 = 1 + 2 = 3 = sqrt3 Segment BC IS congruent to Segment FE Did I do it right?

  31. phi
    • one year ago
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    they are congruent, but you check 2*2 is 4 (not 2)

  32. anonymous
    • one year ago
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    oh yeah oops sqrt5 sqrt5

  33. anonymous
    • one year ago
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    So now what do I do?

  34. phi
    • one year ago
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    what two sides are left to check?

  35. anonymous
    • one year ago
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    FG and AB

  36. phi
    • one year ago
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    yes

  37. anonymous
    • one year ago
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    AB: Height 1; Width -2 FG: Height 2; Width 1 Right?

  38. phi
    • one year ago
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    yes

  39. anonymous
    • one year ago
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    AB 1*1 + -2*-2 = 1+4 = 5 = sqrt5 FG 2*2 + 1*1 = 4+1 = 5 = sqrt5 Segment AB IS congruent to Segment FE Right?

  40. phi
    • one year ago
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    yes. I think there is a theorem that says if all 4 sides are congruent , then the two figures are congruent. But we don't have to use it. if we show that BD = HF (the diagonals) then that shows the triangles match by SSS, and I know that definitely is true.

  41. anonymous
    • one year ago
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    So I just say that they are congruent because BD=HF by SSS or do I write what we did?

  42. phi
    • one year ago
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    BD=HF by doing the same thing: both are 3 width and 3 height so each is sqrt(18) long and therefore congruent.

  43. phi
    • one year ago
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    so we know that triangle BCD can be laid directly on top of triangle FEH because they are congruent by SSS we also know triangle BAD can be laid on top of triangle FGH because they are congruent. when we do that , we see that the shape ABCD lies directly on top of GFEH proving they are congruent.

  44. anonymous
    • one year ago
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    Oh okay thank you @phi I appreciate you making me able to understand this.

  45. phi
    • one year ago
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    yw

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