Video Transcript
The figure shows two triangles,
๐ด๐ต๐ถ and ๐ด prime ๐ต prime ๐ถ prime. Work out the measure of angle
๐ด๐ต๐ถ. What does the AA criterion tell
us about these two triangles?
In this question, we have two
triangles drawn on grid paper. And the first thing weโre asked
to do is find the measure of angle ๐ด๐ต๐ถ, which is in the smaller triangle. In order to do this, we should
recall that the angles in a triangle add up to 180 degrees. Weโll therefore need to
calculate 180 degrees subtract the other two angles of 114.3 degrees and 34.1
degrees, which gives 31.6 degrees. And so thatโs our answer for
the measure of angle ๐ด๐ต๐ถ.
In the second part of this
question, weโre asked about the AA criterion, which is the criterion we use to
show that two triangles are similar. Itโs what we have when we
demonstrate that there are two pairs of angles congruent. So, letโs have a closer look at
these two triangles. The angle ๐ด๐ต๐ถ that weโve
just worked out as 31.6 degrees has a corresponding angle at angle ๐ด prime ๐ต
prime ๐ถ prime of the same value, 31.6 degrees. We also have another pair of
corresponding congruent angles, the angle ๐ถ prime ๐ด prime ๐ต prime and angle
๐ถ๐ด๐ต, which are both given as 34.1 degrees. Showing that there are two
pairs of corresponding congruent angles or the AA rule, we demonstrate that
these two triangles are similar.
We could therefore answer the
second part of this question with a statement such as this: as both triangles
share two angels of equal measures, they must be similar.
