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 corresponds with ∠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:
- EF corresponds with IJ, but EF ≠ IJ
- FG corresponds with JK, but FG ≠ JK
- GH corresponds with KL, but GH ≠ KL
- HE corresponds 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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