medians of a triangle

Front

What is a median of a triangle?

Back

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

Front

What is the point of intersection of the medians called?

Back

The point of intersection of the medians is called the centroid.

Front

What is the property of the centroid in relation to the medians?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

If a triangle has vertices A(0,0), B(6,0), and C(3,6), what is the length of the median from vertex A to side BC?

Back

The length of the median from vertex A to side BC is 5 units.

Front

What is the formula to find the length of a median in a triangle?

Back

The length of a median can be calculated using the formula: m_a = 1/2 * sqrt(2b^2 + 2c^2 - a^2), where a, b, and c are the lengths of the sides.

Front

What is the relationship between the medians and the area of a triangle?

Back

The area of a triangle can be expressed in terms of its medians using the formula: Area = (4/3) * sqrt(s_m * (s_m - m_a) * (s_m - m_b) * (s_m - m_c)), where s_m is the semi-perimeter of the medians.

Front

If the lengths of the sides of a triangle are 7, 8, and 9, what is the length of the median to the side of length 9?

Back

The length of the median to the side of length 9 is approximately 6.93 units.

Front

What is the centroid's location in relation to the triangle's vertices?

Back

The centroid is located at the average of the coordinates of the triangle's vertices.

Front

How does the median affect the balance of a triangle?

Back

The centroid, where the medians intersect, is the triangle's center of mass, balancing the triangle.