# Question Video: Finding the Length of the Base of an Isosceles Triangle Using Its Properties Mathematics

In the figure, what is the length of line segment πΈπΊ?

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### Video Transcript

In the figure, what is the length of line segment πΈπΊ?

In the diagram, we can observe that we have the triangle π·πΈπΊ, which has the line π·πΉ passing through it. Given that we have two line segments that are both given as 10.5 length units, then we know that these sides are congruent. And by definition, that means that triangle π·πΈπΊ is an isosceles triangle.

Now, letβs consider the line π·πΉ. From the markings on the diagram, we notice that line π·πΉ, which passes through the vertex π·, meets the base of line segment πΈπΊ at 90 degrees. And we can recall an important theorem regarding these properties.

It is that the straight line that passes through the vertex angle of an isosceles triangle and is perpendicular to the base bisects the base and the vertex angle. So, because the angle at the vertex is bisected, then the measure of angle πΊπ·πΉ equals the measure of angle πΈπ·πΉ.

And importantly for this question, we know that the base is bisected. So the line segment πΈπΉ has the same length as line segment πΊπΉ, which is 6.5 length units.

We are asked to find the length of the line segment πΈπΊ, which we can find by adding the two lengths on the base. And 6.5 plus 6.5 gives us the answer that the length of line segment πΈπΊ is 13, or 13 length units.