a Start with drawing a triangle. Then, use two rulers to draw a segment parallel to its one side.
B
b Use a ruler to measure appropriate lengths and evaluate the ratios.
C
c What can you say about the ratios you found in the previous part?
A
a See solution.
B
b See solution.
C
c The segments created by a line parallel to one side of a triangle and intersecting the other two sides are proportional.
Practice makes perfect
a We will begin with drawing a triangle ABC.
Next, we will draw the segment DE that will be parallel to AC. To do this, we can use two rulers. One of the rulers will be held still on a piece of paper and the other one will be moved along the first to get parallel lines.
Let's move the horizontal ruler up along the ruler on the left side. After that, draw a segment DE that will intersect two sides of △ ABC. Using this method we can be sure that the segment DE will be parallel to AC.
Finally our diagram is done.
b Now, we are asked to measure and record the lengths AD,DB,CD and EB and evaluate the ratios ADDB and CEEB. Let's use a ruler and start with AD.
We will measure the rest of lengths in the same way.
Now, as we know all the lengths, let's evaluate the ratios of corresponding parts.
Ratio
Substitute and simplify
AD/DB
1.7/2.9≈0.58
CE/EB
1.8/3.1≈0.58
c Looking at the table we made in Part B, we can see that the ratios of corresponding parts are constant. Therefore, we can assume that the segments created by a line parallel to one side of a triangle and intersecting the other two sides are proportional.
