How do you find the third median of a triangle?

First, the Theorem: Apollonius’s Theorem states that in any triangle, the sum of the squares on any two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side.

What is the maximum number of medians of a triangle?

Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle’s centroid. In the case of isosceles and equilateral triangles, a median bisects any angle at a vertex whose two adjacent sides are equal in length.

How do you find the length of a median of a triangle with sides?

The different ways to find the length of a median are as follows: The formula for the length of the median to side BC = 1 2 2 A B 2 + 2 A C 2 − B C 2 \frac{1}{2}\sqrt{2AB^{2}+2AC^{2}-BC^{2}} 212AB2+2AC2−BC2.

What is the formula for median of a triangle?

What is the Median of a Triangle? A line segment, joining a vertex to the mid-point of the side opposite to that vertex, is called the median of a triangle. In the figure given below, AD is the median, dividing BC into two equal parts, such that, BD = DC.

What are the medians of a triangle?

A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex. The medians of a triangle are concurrent at a point. The point of concurrency is called the centroid.

How do you find the area of a triangle with median?

Detailed Solution

1. Given: Length of medians is 9 cm, 10 cm, and 11 cm.
2. Formula used/Concept Used: The formula used to calculate the area of triangles when length of medians is given. s = (u + v + w)/2.
3. Calculation: Length of median is 9 cm, 10 cm, and 11 cm. ∴ s = (9 + 10 + 11)/2 = 15 cm.

Are medians of a triangle equal?

Medians of an Equilateral Triangle are Equal Since the lengths of all sides in an equilateral triangle are the same, the length of medians bisecting these sides are equal.