Video: Finding the Length of a Line Segment in an Isosceles Triangle Using Its Properties

Video Transcript

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

The first thing we wanna do here is take stock of what we’re given in the figure. We have a triangle 𝑋𝑍𝑊. The length of line segment 𝑋𝑊 is equal to the length of line segment 𝑋𝑍, which is equal to 17. We could also say that this is therefore an isosceles triangle. In addition to that, we know that angle 𝑋𝑌𝑍 is a right angle. Based on this given information, we can draw some conclusions. Because we know that line segment 𝑋𝑊 is equal in length to line segment 𝑋𝑍 and we know that angle 𝑋𝑌𝑍 is 90 degrees, we can say that line segment 𝑋𝑌 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 — for us, the point 𝑋 is equidistant from 𝑊 and 𝑍 — then the point is on the perpendicular bisector of the segment, which means we can say that line segment 𝑌𝑍 will be equal in length to line segment 𝑊𝑌, because of the definition of the perpendicular bisector, which divides the line segment it intersects in half. Because line segment 𝑌𝑍 equals 11, we can say that line segment 𝑊𝑌 will also be equal to 11.