Question

read the proof that shows that the medians of an isosceles triangle meet at a point. link here complete the statement about how to prove that the medians of an isosceles triangle meet at a point. to prove that the medians of an isosceles triangle meet at a point, show that the of a side lies on the line containing the opposite and the point where the other two intersect.

Explanation:

To prove that the medians of a triangle (including isosceles) meet at a point (the centroid), we use the property that a median connects a vertex to the midpoint of the opposite side. The general method to show three medians concur is to show that the midpoint of one side lies on the line containing the opposite vertex and the intersection of the other two medians. For an isosceles triangle, we follow the same logic about medians: a median is from a vertex to the midpoint of the opposite side. So the first blank should be "midpoint" (since a median starts at a vertex and goes to the midpoint of the opposite side, and to show concurrency, we show the midpoint of a side lies on the line from the opposite vertex through the intersection of the other two medians), the second blank is "vertex" (the opposite vertex to the side's midpoint), and the third blank is "medians" (the other two medians intersect at a point, and we show the midpoint - vertex line passes through that intersection).

Answer:

First blank: midpoint
Second blank: vertex
Third blank: medians