MATH 120 Lecture Notes - Lecture 34: Street Light, Hot Air Balloon, Protractor
Dr. Matthew M. Conroy - University of Washington
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Similar Triangles Examples
The method of similar triangles comes up occasionally in Math 120 and later courses.
In one phrase, the idea of the method is this: the ratio of corresponding sides of triangles with
the same shape are equal.
Triangles have the same shape if they have the same angles. Since the angles in a triangle
sum to 180◦=πradians, if two angles are known, the third is determined. As a result, if two
triangles have two angles in common, they have the third as well, and so have the same shape.
Two triangle that have the same shape are called similar.
For example, in the picture below, the two triangles are similar.
You could check with a protractor that the angles on the left of each triangle are equal, the
angles at the top of each triangle are equal, and the angles on the right of each triangle are
equal.
As a result, the triangles are similar and this means that they have the same shape. This means
that one is a scaled up version of the other (in fact, the large triangle is exactly the smaller one
scaled up by a factor of 2: the sides of the large triangle are twice as long as the corresponding
sides of the smaller triangle). Note that when we scale up, or scale down, a triangle, the angles
do not change.
The most common way to we see similar triangle in Math 120 or in calculus courses is when
we have to right triangles that overlap, like this:
find more resources at oneclass.com
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Document Summary
The method of similar triangles comes up occasionally in math 120 and later courses. In one phrase, the idea of the method is this: the ratio of corresponding sides of triangles with the same shape are equal. Triangles have the same shape if they have the same angles. Since the angles in a triangle sum to 180 = radians, if two angles are known, the third is determined. As a result, if two triangles have two angles in common, they have the third as well, and so have the same shape. Two triangle that have the same shape are called similar. For example, in the picture below, the two triangles are similar. You could check with a protractor that the angles on the left of each triangle are equal, the angles at the top of each triangle are equal, and the angles on the right of each triangle are equal.
