Medians & Altitudes

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

What is an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

What is the difference between a median and an altitude?

Back

A median connects a vertex to the midpoint of the opposite side, while an altitude is perpendicular to the opposite side.

Front

How do you find the length of a median?

Back

To find the length of a median, use the formula: m = 1/2 * √(2a² + 2b² - c²), 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 medians of a triangle?

Back

The three medians of a triangle intersect at a point called the centroid, which divides each median into a ratio of 2:1.

Front

What is the centroid of a triangle?

Back

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

Front

If a triangle has sides of lengths 6, 8, and 10, what is the length of the median to the longest side?

Back

The length of the median to the longest side (10) is 7.5.

Front

What is an angle bisector?

Back

An angle bisector is a line that divides an angle into two equal parts.

Front

How do you find the length of an angle bisector?

Back

The length of an angle bisector can be found using the formula: d = (2ab)/(a + b) * cos(C/2), where a and b are the lengths of the sides adjacent to the angle, and C is the angle.

Front

What is the significance of the altitude in triangle area calculation?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height, where the height is the length of the altitude.