Video Transcript
Which of the following triangles is similar to the one seen in the given figure?
We can begin by recalling what we mean by similar triangles. Similar triangles have all three pairs of corresponding angles congruent and all
three pairs of corresponding sides in proportion. If we want to prove that two triangles are similar, we can either prove that all the
corresponding pairs of angles are congruent or that all the corresponding pairs of
sides are in proportion. So let’s take a look at the figure we are given.
We have an angle with a measure of 100 degrees and another angle with a measure of 30
degrees. Now, none of the triangles in the answer options have angles of 30 degrees and 100
degrees. So, if we want to find a similar triangle from one of these options, we need to
consider the third angle measure in our given triangle.
We know that the angle measures in a triangle sum to 180 degrees. So the third angle measure must be equal to 180 degrees minus the sum of 100 degrees
and 30 degrees. That’s 180 degrees minus 130 degrees, which is 50 degrees. Options (A), (B), (C), and (D) don’t have the correct angle measures, but option (E)
does. It has two measures of 50 degrees and 30 degrees. And we know that 30 degrees, 50 degrees, and 100 degrees add to 180 degrees. So the third angle is 100 degrees. Therefore, it is the triangle given in option (E) that is similar to the given
triangle.
Although we worked out the measures of all three angles in these two triangles, it is
sufficient to demonstrate that just two pairs of angles in a triangle are congruent
to prove that the triangles are similar, since if two pairs of angles are congruent,
then the remaining pair of angles are also congruent.
