Two congruent plane figures: exercise 2

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:

Second, in every tip of the trapezoids, I give a letter. Then I will get trapezoid ABCD, trapezoid EFGH, and trapezoid WXYZ.

∠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.

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.

∠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.

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.

∠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.

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.

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).

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Ibnu Kahfi

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