Video Transcript
The figure shows two
triangles. Are the two triangles
similar? Why?
In this question, we’re asked
if these two triangles are similar. We can recall that similar
triangles have corresponding angles congruent and corresponding sides in
proportion. So, let’s have a look at the
angles in both of these triangles. There’s a right angle of 90
degrees in each triangle. And one triangle has a
60-degree angle, and the other one has a 30-degree angle. However, if we remember that
the angles in a triangle add up to 180 degrees, then we could calculate the
third angle in each triangle.
In the top triangle, 60 plus
the right angle of 90 degrees would give us 150 degrees, and subtracting that
from 180 degrees would leave us with 30 degrees. In the lower triangle, 90
degrees plus 30 gives us 120 degrees, leaving us with a third angle of 60
degrees. What we can see then is that we
have three pairs of equal angles. We have two 30-degree angles,
two 60-degree angles, and two 90-degree angles. We have shown a three pairs of
corresponding angles congruent. But in fact, we only need to
show two pairs of corresponding angles congruent in order to show that two
triangles are similar.
So, to answer the question “are
the two triangles similar?” is yes. To answer the second question
“why?,” we could say that if you calculate the measure of the third angle in one
of the triangles, you can see that the triangles share two angles. Therefore, by the AA criteria,
the triangles are similar.
