Sunday 23 November 2014

Two congruent plane figures: exercise 1

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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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