How many maximum medians does a triangle have?

How many maximum medians does a triangle have?

three medians
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle’s centroid.

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.

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.

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 many vertices and medians can triangle have?

A triangle has three vertices. From each vertex, one median can be drawn. So, there are three medians in a triangle.

What is the length of medians?

7. In an isosceles triangle, medians drawn from equal angles are equal in length. The length of medians drawn from vertices with equal angles should be equal. Thus, in an isosceles triangle, ABC if AB = AC, medians BE, and CF originating from the vertex B and C respectively are equal in length.

How do you find the equation of the median of a triangle?

Step 3: The length of the median can be calculated with the distance formula, D = √[(x2 – x1)2 + (y2 – y1)2]; where (x1, y1) and (x1, y1) are the coordinates of the median.

How do you find the centroid of a triangle with medians?

Cut a triangle of any shape out of a fairly stiff piece of cardboard. Carefully find the midpoints of two of the sides, and then draw the two medians to those midpoints. The centroid is where these medians cross. (You can draw in the third median if you like, but you don’t need it to find the centroid.)

How do you find the length of the medians of a triangle?

The area of the triangle is divided into half by a median. The triangle is divided into 6 smaller triangles of the same area by the centroid. In an equilateral triangle, the length of the medians is equal. The medians from the vertices having equal angles are of equal length in the case of an isosceles triangle.

What is the relationship between median and length of sides?

The median and lengths of sides are related in such a way that “3 times the sum of squares of the length of sides = 4 times the squares of medians of a triangle.” 3 (AB 2 + BC 2 + CA 2) = 4 (AD 2 + BE 2 + CF 2). All the three medians intersect at one single point that divides the medians’ lengths in the ratio of 2:1.

What is the ratio of the area of triangle ABC to CGF?

Useful Result: The triangle formed by the medians of a given triangle will have an area three-fourths the area of the given triangle. If ABC is a triangle with medians of lengths u, v, and w, and CGF is a triangle with sides the same length as these medians then the ratio of the area of triangle ABC to the area of triangle CGF is 4 to 3.

How do you find the sum of sides of a triangle?

The sum of two sides of a triangle is greater than the median drawn from the vertex, which is common. The median and lengths of sides are related in such a way that “3 times the sum of squares of the length of sides = 4 times the squares of medians of a triangle.” 3 (AB 2 + BC 2 + CA 2) = 4 (AD 2 + BE 2 + CF 2).