### Video Transcript

In the following figure, find the measure of angle π½πΎπΏ.

Letβs begin by looking at the diagram and identifying that angle π½πΎπΏ is part of
the triangle π½πΎπΏ, which is at the top part of this figure. There is also another triangle ππΎπΏ below this in the figure. We can observe that both these triangles are in fact right triangles, since the two
angles of πΏπ½πΎ and πΏππΎ both have measures of 90 degrees.

Next, we can see from the markings on the triangles that the line segment π½πΏ is
congruent to the line segment ππΏ. We might wonder at this point if the triangles π½πΎπΏ and ππΎπΏ are congruent to
each other. As both of these triangles are right triangles, we can consider if the right
angle-hypotenuse-side, or RHS, criterion would apply.

The line segment πΎπΏ is the hypotenuse in both triangles. And since it is common to both triangles, then we know that it is congruent in
each. So we have demonstrated that there is a pair of right angles. The hypotenuse in each triangle is congruent. And there is another pair of congruent sides. We have therefore proved that triangle π½πΎπΏ is congruent to triangle ππΎπΏ by the
RHS congruence criterion.

We note that angles π½πΎπΏ and ππΎπΏ are corresponding. So the measure of angle π½πΎπΏ is the same as the measure of ππΎπΏ. They are both 34 degrees. So, by first proving that the triangles were congruent, we have found the unknown
angle measure of π½πΎπΏ as 34 degrees.