Two congruent plane figures: exercise 1

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:
• ∠PQR corresponds with ∠XYZ, then∠PQR = ∠XYZ = 100⁰
• ∠QRS corresponds with ∠YZW, then∠QRS = ∠YZW = 80⁰
• ∠RSP corresponds with ∠ZWX, then ∠RSP = ∠ZWX = 100⁰
• ∠SPQ corresponds 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:
• PQ corresponds with WX, but PQ ≠ WX.
• QR corresponds with XY, then QR = XY.
• RS corresponds with YZ, but RS ≠ YZ.
• SP corresponds 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

Related Articles:

Mathematics

• The Congruence of Two Plane Figures.
• How to Determine the Length of Sides and the Size of Angles.
• Two Congruent Plane Figures: Exercise 2.
• Two Congruent Plane Figures: Exercise 3.
• Two Congruent Plane Figures: Exercise4.

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