Sunday, 23 November 2014

Two congruent plane figures: exercise 2

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Catatan ke-8


Exercise
Consider the plane figures below! Show the couples of the congruent figures? Explain step by step the answer.



Answer:
  • First of all, I must to know the requirements for the congruence of two plane figures. That are:
    • The corresponding lengths are equal; and
    • The corresponding angles are similar.
  • Second, in every tip of the trapezoids, I give a letter. Then I will get trapezoid ABCD, trapezoid EFGH, and trapezoid WXYZ. 

  • Fourth, solution for the trapezoid ABCD and EFGH
    • The followings are the size of corresponding angles:
      • ?ABC corresponds with ?FGH, then ?ABC = ?FGH
      • ?BCD corresponds with ?EFG, then ?BCD = ?EFG = x
      • ?CDA corresponds with ?HEF, then ?CDA = ?HEF = y
      • ?DAB corresponds with ?GHE, then ?DAB = ?GHE
      • The corresponding angles have similar sizes. It's mean, one requirement is fulfilled.
    • The followings are the length of corresponding sides:
      • AB corresponds with GH, then AB = GH
      • BC corresponds with FG, then BC = FG
      • CD corresponds with EF, then CD = EF
      • DA corresponds with PQ, then DA = HE
      • I got that the length of the corresponding sides have similar sizes. Hence, one requirement is fulfilled. 

  • Fifth, solution for the trapezoid ABCD and IJKL
    • The followings are the size of corresponding angles:
      • ?ABC corresponds with ?JKL, then ?ABC = ?JKL
      • ?BCD  correspondswith ?IJK, then ?BCD = ?IJK = x
      • ?CDA corresponds with ?LIJ, then?CDA = ?LIJ = y
      • ?DAB corresponds with ?KLI, then ?DAB = ?KLI
      • The corresponding angles have similar sizes. It's mean, one requirement is fulfilled.
    • The followings are the length of corresponding sides:
      • AB corresponds with KL, but AB ? KL
      • BC corresponds with JK, but BC ? JK
      • CD corresponds with IJ, but CD ? IJ
      • DA corresponds with LI, but DA ? LI
      • The result, I got that the length of the corresponding sides are not similar. Hence, one requirement is not fulfilled. 

  • Sixth, solution for the trapezoid EFGH and IJKL
    • The followings are the size of corresponding angles:
      • ?EFG corresponds with ?IJK, then ?EFG = ?IJK = x
      • ?FGH corresponds with ?JKL, then ?FGH = ?JKL
      • ?GHE corresponds with ?KLI, then ?GHE = ?KLI
      • ?HEF corresponds with ?LIJ, then ?HEF = ?LIJ =  y
      • The corresponding angles have similar sizes. It's mean, one requirement is fulfilled.
    • The followings are the length of corresponding sides:
      • EFcorresponds with IJ, but EF ? IJ
      • FGcorresponds with JK, but FG ? JK
      • GHcorresponds with KL, but GH ? KL
      • HEcorresponds with LI, but HE ? LI
      • The length of the corresponding sides has different sizes. Hence, one requirement is not fulfilled. 

  • Based on the description above I can conclude as follow:
    • The trapezoid ABCD is congruent with the trapezoid EFGH, because two requirements for the congruence of two plane figures are fulfilled.
    • The trapezoid ABCD is not congruent with the trapezoid IJKL because one of requirement is not fulfilled, that is the corresponding sides is not in equal size (AB ? KL, BC? JK, CD ? IJ, and DA ? LI).
    • The trapezoid EFGH is not congruent with the trapezoid IJKL because one of requirement is not fulfilled, that is the corresponding sides is not in equal size (GH ? KL, FG ? JK, EF ? IJ, and HE ? LI).


Happy blogging!

Ibnu Kahfi

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