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

# Question Video: Finding the Length of a Line Segment in an Isosceles Triangle Using Its Properties Mathematics • Second Year of Preparatory School

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In the figure, find the length of line segment ππ.

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### Video Transcript

In the following figure, find the length of line segment ππ.

The first thing we wanna do here is take stock of what weβre given in the figure. We have a triangle πππ. The length of line segment ππ is equal to the length of line segment ππ, 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π is a right angle. Based on this given information, we can draw some conclusions. Because we know that line segment ππ is equal in length to line segment ππ and we know that angle πππ is 90 degrees, we can say that line segment ππ 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 ππ will be equal in length to line segment ππ, because of the definition of the perpendicular bisector, which divides the line segment it intersects in half. Because line segment ππ equals 11, we can say that line segment ππ will also be equal to 11.

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