Final answer:
To prove that in an isosceles triangle two medians are equal, we can use the concept of congruent triangles.
Step-by-step explanation:
To prove that in an isosceles triangle two medians are equal, we can use the concept of congruent triangles. Let's assume the isosceles triangle ABC, where AB = BC and M is the midpoint of AB.
First, draw the median CM. Now, let's draw the perpendicular bisector of BC, and label its intersection with CM as O. Since the triangle ABC is isosceles, we know that angle BMC is congruent to angle BAC.
By definition of congruent triangles, angles BMO and AMO are also congruent. This means that the triangles BMC and BMO are congruent.
Now, using congruent triangles, we can conclude that BM = MO. Similarly, we can prove that the median AM is equal to MO. Hence, in an isosceles triangle, two medians are equal.