Homework 5-5 Median & Altitude

Front

What is a centroid in a triangle?

Back

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

Front

How do you find the length of a segment in a triangle using the centroid?

Back

The lengths of the segments created by the centroid divide each median into a ratio of 2:1.

Front

If AG = 3x + 15 and BG = 5x + 9, how do you solve for x?

Back

Set AG equal to BG: 3x + 15 = 5x + 9. Solve for x to find x = 3.

Front

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

Back

The length of a median can be calculated using the formula: m = 1/2 * √(2a² + 2b² - c²), where a, b, and c are the lengths of the sides of the triangle.

Front

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

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

How do you find the value of n in a triangle problem?

Back

Use the properties of triangles, such as the sum of angles or the relationships between sides, to set up an equation and solve for n.

Front

What is the significance of the centroid in triangle geometry?

Back

The centroid is important because it provides a balance point for the triangle and is used in various applications, including physics and engineering.

Front

If AG = 3x + 15 and BG = 5x + 9, what is the value of AG when x = 3?

Back

AG = 3(3) + 15 = 24.

Front

What is the formula for finding the area of a triangle using the median?

Back

Area = (1/2) * base * height, where the height can be found using the median.

Front

How do you determine the length of a segment in a triangle?

Back

Use the properties of triangles, such as the Pythagorean theorem or the triangle inequality theorem, to find the length.