When the ratio of two line segments is equal to the ratio of two other segments, they are called proportional segments.
A reason between two segments is obtained by dividing the length of one by the other.
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Thus, given four proportional line segments with lengths The, B, w It is d, in that order, we have a proportion:
And, by the fundamental property of proportions, we have .
To learn more, check out a list of exercises on proportional segments, with all questions resolved!
Question 1. The segments are, in that order, proportional segments. Determine the measure of knowing that , It is .
Question 2. Determine knowing that is that:
Question 3. Determine knowing that is that:
Question 4. Determine the lengths of the sides of a triangle that has a perimeter of 52 units and whose sides are proportional to the sides of another triangle with lengths 2, 6, and 5.
If the segments are, in that order, proportional segments, then:
replacing , It is , We have to:
Applying the fundamental property of proportions:
We have:
replacing , We have to:
Applying the fundamental property of proportions:
We have:
As , then, . Substituting in the above expression, we have:
Applying the fundamental property of proportions:
Soon .
Making a representative drawing, we can see that .
Since the sides of the triangles are proportional, we have:
Being the ratio of proportionality.
Furthermore, if the sides are proportional, their sum, that is, the perimeters, are also:
From the ratio of proportionality and the known sides, we obtain the measures of the sides of the other triangle:
To download this list of exercises on proportional segments in PDF, click here!
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