### Video Transcript

In the following figure, find the
length of line segment ππ.

The first thing we wanna do here is
take stock of what weβre given in the figure. We have a triangle πππ. The length of line segment ππ is
equal to the length of line segment ππ, which is equal to 17. We could also say that this is
therefore an isosceles triangle. In addition to that, we know that
angle πππ is a right angle. Based on this given information, we
can draw some conclusions. Because we know that line segment
ππ is equal in length to line segment ππ and we know that angle πππ is 90
degrees, we can say that line segment ππ is a perpendicular bisector.

We can make this claim based on the
converse of the perpendicular bisector theorem. That tells us if a point is
equidistant from the endpoints of a segment β for us, the point π is equidistant
from π and π β then the point is on the perpendicular bisector of the segment,
which means we can say that line segment ππ will be equal in length to line
segment ππ, because of the definition of the perpendicular bisector, which divides
the line segment it intersects in half. Because line segment ππ equals
11, we can say that line segment ππ will also be equal to 11.