Catatan ke-6
A. Exercise
Consider the plane figures below, show the couples of the congruent figures?
Answer:
- First to all, I have 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 quadrilaterals, I give a letter. Thus, I get the rectangle ABCD, the rectangle PQRS, and the rectangle WXYZ.
- Third, solution for the rectangle ABCD and PQRS.
- The followings are the size of corresponding angles:
- ∠ABC corresponds with ∠PQR, then ∠ABC = ∠PQR = 1000
- ∠BCD corresponds with ∠QRS, then ∠BCD = ∠QRS = 800
- ∠CDA corresponds with ∠RSP, then ∠CDA = ∠RSP = 1000
- ∠DAB corresponds with ∠SPQ, then ∠DAB = ∠SPQ = 800
- Thus, the corresponding angles has the similar size. It's mean, one requirement is fulfilled.
- The followings are the length of corresponding sides:
- AB corresponds with QR, then AB = QR
- BC corresponds with RS, but BC ≠ RS
- CD corresponds with SP, then CD = SP
- DA corresponds with PQ, but DA ≠ PQ
- I got the corresponding sides has two similar length and two different length. Hence, one requirement is not fulfilled.
- Fourth, solution for the rectangle ABCD and WXYZ.
- The followings are the size of corresponding angles:
- ∠ABC corresponds with ∠XYZ, then ∠ABC = ∠XYZ = 1000
- ∠BCD corresponds with ∠YZW, then ∠BCD = ∠YZW = 800
- ∠CDA corresponds with ∠ZWX, then ∠CDA = ∠ZWX = 1000
- ∠DAB corresponds with ∠WXY,then ∠DAB = ∠WXY= 800
- The corresponding angles have the same sizes. It's mean, one requirement is fulfilled.
- The followings are the length of corresponding sides:
- AB corresponds with XY, then AB = XY
- BC corresponds with YZ, then BC = YZ
- CD corresponds with ZW, then CD = ZW
- DA corresponds with WX, then DA = WX
- The result, I got corresponding sides are also similar. One requirement is fulfilled.
- Fifth, solution for the rectangle PQRS and WXYZ.
- The followings are the size of corresponding angles:
- ∠PQRcorresponds with ∠XYZ, then∠PQR= ∠XYZ = 1000
- ∠QRScorresponds with ∠YZW, then∠QRS= ∠YZW = 800
- ∠RSPcorresponds with ∠ZWX, then ∠RSP= ∠ZWX = 1000
- ∠SPQcorresponds with ∠WXY, then ∠SPQ = ∠WXY = 800
- The corresponding angles has similar sizes. It's mean, one requirement is fulfilled.
- The followings are the length of corresponding sides:
- PQcorresponds with WX, but PQ ≠ WX.
- QRcorresponds with XY, then QR = XY.
- RScorresponds with YZ, but RS ≠ YZ.
- SPcorresponds with ZW, thenSP = ZW.
- I got two similar sizes and two different sizes. Thus, one requirement is not fulfilled.
- Based on the description above, I can conclude as follow:
- The rectangle ABCD is not congruent with the rectangle PQRS because one of requirement is not fulfilled, that is the corresponding sides is not equal in size (BC ≠ RS and DA ≠ PQ).
- The rectangle PQRS is not congruent with the rectangle WXYZ because one of requirements is not fulfilled, that is the corresponding sides is not equal in size (PQ ≠ WX and RS≠ YZ).
- If two requirements for the congruence of two plane figures are fulfilled, thus the rectangle ABCD and the rectangle WXYZ are congruent.
Happy blogging!
Ibnu Kahfi
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