Saturday 18 October 2014

The Congruence of Two Plane Figures

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Catatan ke-2


A. Introduction
Before you study the congruence of two plane figures, you have to know about plane figure or two dimensions.

Plane figure is geometric figure that all parts placed in one plane. Examples: right, triangle, square, rectangle, parallelogram, trapezoid, pentagonal, circle, and ellipse.


B. The Congruence of Two Plane Figures
The congruence of two plane figures are two plane figures that have equal form and size, pressed to each other, then they will closed with exactly.


C. The Requirements
The requirements for the congruence of two plane figures:
  1. The corresponding lengths are equal,
  2. The corresponding angles are similar.

As notes:
  • If the corresponding lengths are equal, then the proportion of them, must be 1:1;
  • If one's of two requirements aren't achieved, means the two plane figures are not congruent.


D. The Example Question
Can you determine the couples of the rectangle ABCD and EFGHare congruent or not?



Answer:
Based on the figures above, we have the rectangle ABCD and EFGH. Then, solution for the question above are:
  • First, we have to find the equal lengths. Determine whether the equal lengths are corresponds or not! The followings are the lengths of the corresponding sides:
    • AB corresponds with EF, so AB = EF = 8 cm,
    • BC corresponds with FG, so BC = FG = 3 cm,
    • CD corresponds with GH, so CD = GH = 8 cm,
    • DA corresponds with HE, so DA = HE = 3 cm.
    • We found that the corresponding lengths are equal. One of requirements is achieved. 

  • Second, we have to find the similar angles. Determine whether the angles are corresponds or not! The followings are the corresponding angles:
    • ?ABC corresponds with ?EFG, so ?ABC = ?EFG = 90�,
    • ?BCD corresponds with ?FGH, so ?BCD = ?FGH = 90�,
    • ?CDA corresponds with ?GHE, so ?CDA = ?GHE = 90�,
    • ?DAB corresponds with ?HEF, so ?DAB = ?HEF = 90�.
    • We found the corresponding angles are similar size. And also, either requirement is achieved.

  • Finally, the couples of the rectangle ABCD and the rectangle EFGH are congruent.


Happy blogging!

Ibnu Kahfi


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