Related article(s): Plane geometry: The requirements for the drawing - an overview
In the previous article about an overview of the requirements for the plane geometry drawing mentioned the requirements for accuracy, scientific and aesthetics. This article will further analyse the first requirement: accuracy! Accuracy in drawing is especially important and reflected in the following key points:
1) Angles with a given value as of 90 °, 60 °, 45 °, 30 °, ... need to be accurately constructed. Or an angle bisector must divide that angle into two congruent parts,... Let’s look at the diagram Pic 1:
Suppose ΔABC = ΔJIK and 2 straight lines AD and IL are the bisector of the angle BAC and JIK respectively. Did you think that both figures were correct?
 |
| Pic 1: AD is the bisector of angle BAC and IL is the angle bisector of JIK |
Next, draw two circles C1, C2 of center D and L that are tangent to the rays of ∠BAC and ∠JIK respectively! Pic 2 shows what would happen:
 |
| Pic 2: Draw a circle of center D, tangent to AB and a circle of center L, tangent to IJ |
C1 touches both rays AB and AC while C2 only touches IJ but not IK! The problem is that bisector IL is drawn incorrectly (specifically in this case ∠JIL < ∠LIK). Clearly, although looking at pic 1, both figures seem to be good, the 2nd picture in fact is inaccurate and will not allow us to continue to solve the problem as figure Pic 2.
2) Accuracy is also reflected in the correlation in length of the line segments. For example, given the triangle ΔABC with AC > AB, in the drawing, the length of AC should be greater than AB. If given two straight lines of equal length, then their lengths must be equal in the drawing. Or if you draw two perpendicular lines, the angle created by two lines in the figure must be exactly 90°. For example, take a look at the figure below:
 |
| Pic 3: Given ΔABC, angle A = 90° |
Which triangle is correctly drawn? Are both or either correct? Given angle A is a right angle, hence if we draw a circle of diameter BC, then A will be one of the points on such circle. We have:
 |
| Pic 4: for ΔABC, angle A = 90°, draw a circle of diameter BC |
Figure Pic 4 showed that apparently the below triangle in Figure Pic 3 is not correct. And if we continue to draw, the figure would become unreasonable. Those above are just two of many examples showing that if we did not draw accurately, we could not continue to study or solve geometric problems. The accuracy in drawing is absolutely important and is the first requirement!
No comments:
Post a Comment