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

In the figure, find the length of line segment π‘Šπ‘Œ.

01:34

Video Transcript

In the following figure, find the length of line segment π‘Šπ‘Œ.

The first thing we wanna do here is take stock of what we’re given in the figure. We have a triangle π‘‹π‘π‘Š. The length of line segment π‘‹π‘Š 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 π‘‹π‘Œπ‘ is a right angle. Based on this given information, we can draw some conclusions. Because we know that line segment π‘‹π‘Š is equal in length to line segment 𝑋𝑍 and we know that angle π‘‹π‘Œπ‘ is 90 degrees, we can say that line segment π‘‹π‘Œ 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 𝑋 is equidistant from π‘Š and 𝑍 β€” then the point is on the perpendicular bisector of the segment, which means we can say that line segment π‘Œπ‘ will be equal in length to line segment π‘Šπ‘Œ, because of the definition of the perpendicular bisector, which divides the line segment it intersects in half. Because line segment π‘Œπ‘ equals 11, we can say that line segment π‘Šπ‘Œ will also be equal to 11.

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