Catatan ke-4
A. Introduction
Before you study this subject, first of all, you must be understood about the definition of two congruent plane figures. Why? Because the next subject, we learn to deepen about the congruence of two plane figures.
Okay. We will learn subject about how to determine the length of sides and the size of angles on two congruent plane figures.
B. The Corresponding Length of Sides
To determine the length of sides from two congruent plane figures, first of all, we have to know the corresponding lengths. If you find in the exercises, there isn't explain about congruent or not, you have to determine whether two plane figures, congruent or not! And then, you can determine the length of sides.
C. Some Example Questions for The Corresponding Length of Sides
Example 1.
In the figures below, the rectangle ABCD and the rectangle EFGH are congruent. The length of AB = 12 cm and EF = 3 cm. Decide the length of BC, DA, FG, and GH?
Answer 1:
Based on the figures above, we know that:
- First, the couples of two plane figures are congruent.
- Second, the corresponding lengths:
- AB corresponds with FG, so AB = FG
- BC corresponds with GH, so BC = GH
- CD corresponds with HE, so CD = HE
- DA corresponds with EF, so DA = EF
- Third, since rectangle ABCD and rectangle EFGH are congruent, so we have:
- The length of AB = FG CD = HE = 12 cm
- The length of EF = DA = BC = GH = 3 cm
- Finally, the length of BC = 3 cm, DA = 3 cm, FG = 12 cm, and GH = 3 cm.
Example 2.
Show the plane figures below! There are the square IJKL and the quadrilateral MNOP. The length of KL = 4 cm and OP = 4 cm. Decide the value of MN and NO?
Answer 2.
- Based on the question above, we don't know whether two plane figures are congruent or not! If they are congruent, we can solve the question. If they are not congruent, we can not find the lengths of MN and NO.
- From the figures above, we get the corresponding lengths and not the corresponding length:
- IJ corresponds with MN, then IJ = MN
- JK is not corresponds with NO, then JK ≠ NO
- KL corresponds with OP, then KL = OP
- LI is not corresponds with PM, then LI ≠ PM
- Due to one requirement of two congruent plane figures is not fulfilled, that is the corresponding length is not similar. Then, the square IJKL and quadrilateral MNOP aren't congruent. Thus, we can not solve the question.
D. The Corresponding Size of Angles
To determine the size of angles from two congruent plane figures, we have to use one requirement that is the corresponding angles must be equal. If the requirements are not achieve, two plane figures are not congruent.
E. The Example Question for The Corresponding Size of Angles
Example 3.
Let the couples of two congruent plane figures, rectangle ABCD and rectangle EFGH. If ∠ABC = 90°, decide the size of ∠CDA, ∠HEF, and ∠BCD?
Answer 3.
- From the question above, we knew that the rectangle ABCD and EFGH are congruent. Then, we can get the corresponding angles:
- ∠ABC corresponds with ∠FGH, then ∠ABC = ∠FGH = 90°
- ∠BCD corresponds with ∠GHE, then ∠BCD = ∠GHE
- ∠CDA corresponds with ∠HEF, then ∠CDA = ∠HEF
- ∠DAB corresponds with ∠EFG, then ∠DAB = ∠EFG
- Due to ∠ABC and ∠FGH are right angles, so the size of ∠CDA = ∠HEF = ∠BCD = 90°.
Happy blogging!
Ibnu Kahfi
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