# How do you prove the median of a triangle?

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## How do you prove the median of a triangle?

One median We can come up with a conjecture and say that, the median of a triangle divides the triangle into two triangles with equal areas. To show that this is always true we can write a short proof: Area of any triangle = half the base x height.

How do you prove the centroid of a triangle?

Definition: For a two-dimensional shape “triangle,” the centroid is obtained by the intersection of its medians. The line segments of medians join vertex to the midpoint of the opposite side. All three medians meet at a single point (concurrent). The point of concurrency is known as the centroid of a triangle.

Are median of triangle concurrent?

Concurrence of the Medians of a Triangle. The medians of a triangle are concurrent and the point of concurrence, the centroid, is one-third of the distance from the opposite side to the vertex along the median.

### How do you prove the centroid of a triangle divides the median in 2 1?

Now Here G is the centroid of the triangle and AD, BE, CF are the medians. Thus, the centroid of the triangle divides each of the median in the ratio 2:1. Therefore, Option (C) is correct.

What are the 3 medians of a triangle?

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.

Does a median divide a triangle into two equal parts?

Let AD be one of its medians. ∆ABD and ∆ADC have the vertex A in common. Hence, the bases BD and DC are equal (as AD is the median). Hence the median of a triangle divides it into two triangles of equal areas.

## Why is the centroid of a triangle 1 3?

The centroid is the point where the three medians of the triangle intersect. The centroid is located 1/3 of the distance from the midpoint of a side along the segment that connects the midpoint to the opposite vertex. For a triangle made of a uniform material, the centroid is the center of gravity.

Can you have a triangle with two obtuse angles?

We have the property that the sum of the angles of a triangle is always 180∘ . Obtuse angle is an angle which has magnitude more than 90∘ . So adding that two angles only we will get 180∘ or more than that. Hence having two angle obtuse, construction of a triangle is not at all possible.

How to find the median of a triangle?

How to Find the Median of a Triangle A theorem called Apollonius’s Theorem gives the length of the median of a triangle. According to the theorem: ‘the sum of the squares of any two sides of a triangle equals twice the square on half the third side and twice the square on the median bisecting the third side’.

### Are the medians of an isosceles triangle always the same length?

In an isosceles triangle, the two medians drawn from the vertices of the equal angles are equal in length. d. In a scalene all the medians are of different length. e. The medians are always inside the triangle. 1. MEDIANS AND AREA

How can you tell if two triangles are the same height?

The two triangles have the same height. From the two areas we see that FE=FE (the two triangles have the same height). Also AM=MB (M is the midpoint of AB, since AM is the median of the triangle. This then means that the two triangles are equal in area. Now let us consider two medians.

How is the area of a triangle determined?

Earlier on when we considered the case of two medians we saw that the second median divided the two triangles formed by the first median in the ratio 2:1. Using that argument we know that the area of triangle AED is 1/3 the area of triangle CAD.