Midsegments and Medians and more

Front

What is the definition of a centroid in a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it is also the center of mass of the triangle.

Front

How do you find the length of a median in a triangle?

Back

To find the length of a median, use the formula: Median = 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 opposite side.

Front

What is the relationship between the centroid and the lengths of the segments it creates?

Back

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

Front

If the length of segment GE is 7, what is the length of segment BE in triangle ABC?

Back

The length of segment BE is 21, as the centroid divides the median in a 2:1 ratio.

Front

What is the formula for the perimeter of a triangle?

Back

The perimeter of a triangle is the sum of the lengths of all three sides: Perimeter = a + b + c.

Front

How do you calculate the length of a segment in a triangle given the coordinates of its endpoints?

Back

Use the distance formula: Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

Front

What is a median in a triangle?

Back

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

Front

What is the significance of the centroid in triangle geometry?

Back

The centroid is significant because it is the balance point of the triangle and is used in various applications, including physics and engineering.

Front

How do you find the midpoint of a line segment in a triangle?

Back

The midpoint can be found using the formula: Midpoint = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

Front

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

Back

The area of a triangle can be calculated using the lengths of its medians with the formula: Area = (4/3) * sqrt(s * (s - m1) * (s - m2) * (s - m3)), where s is the semi-perimeter of the triangle formed by the medians.