Medians and Midsegments of Triangles

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of a triangle 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 centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect.

Front

What is the relationship between the lengths of segments created by the centroid?

Back

The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle.

Front

What is the relationship between a midsegment and the sides of a triangle?

Back

A midsegment is parallel to the third side of the triangle and its length is half the length of that side.

Front

If the lengths of two sides of a triangle are 10 and 14, what is the length of the midsegment connecting those two sides?

Back

The length of the midsegment is 7, which is half of the length of the third side.

Front

What is the formula for finding the length of a median in a triangle?

Back

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

Front

How do you find the midpoint of a line segment?

Back

The midpoint can be found by averaging the x-coordinates and the y-coordinates of the endpoints: Midpoint M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the significance of the centroid in real-world applications?

Back

The centroid can represent the center of mass or balance point of a triangular object, which is important in engineering and design.