Geometric drawings :
In this section, we will learn, how geometric figures can be drawn with the given conditions.
Example 1 :
Use geometry software to draw a triangle whose sides have the following lengths: 2 units, 3 units, and 4 units.
Step 1 :
Draw the segments.
Step 2 :
Let AB be the base of the triangle. Place point C on top of point B and point E on top of point A.
Step 3 :
Using the points C and E as fixed vertices, rotate points F and D to see if they will meet in a single point.
Note that the line segments form a triangle.
Repeat step 1 and step 2, but use a different segment as the base. Do the segments form a triangle? If so, is it the same as the original triangle ?
Yes; the triangle has the same size and shape as the original.
Use geometry software to draw a triangle with sides of length 2, 3, and 6 units, and one with sides of length 2, 3, and 5 units. Do the line segments form triangles? How does the sum of the lengths of the two shorter sides of each triangle compare to the length of the third side ?
1 st : no, 2 + 3 < 6
2 nd : no; 2 + 3 = 5
Do two segments of lengths a and b units and a longer segment of length c units form one triangle, more than one, or none ?
One triangle if a + b > c ; none if a + b ≤ c.
Example 2 :
Use a ruler and a protractor to draw a triangle for the given measures.
Angles : 30° and 80°
Length of included side : 2 inches
Step 1 :
Use a ruler to draw a line that is 2 inches long. This will be the included side.
Step 2 :
Place the center of the protractor on the left end of the 2-in. line. Then make a 30°-angle mark.
Step 3 :
Draw a line connecting the left side of the 2-in. line and the 30°-angle mark. This will be the 30° angle.
Step 4 :
Repeat Step 2 on the right side of the triangle to construct the 80° angle.
Step 5 :
The side of the 80° angle and the side of the 30° angle will intersect. This is Triangle 1 with angles of 30° and 80° and an included side of 2 inches.
Will a triangle be unique if you know all three angle measures but no side lengths ?
Yes, the two angles and the length of the included side determine the point at which the sides meet. The triangle is unique.
After having gone through the stuff given above, we hope that the students would have understood "Geometric drawings".
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