Medians & Altitudes

Front

What is an altitude in a triangle?

Back

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

Front

What is a median in a triangle?

Back

A median is a 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 relationship between the medians of a triangle and its centroid?

Back

The centroid is the point where all three medians intersect, and it divides each median into a ratio of 2:1.

Front

What is the definition of perpendicular lines?

Back

Perpendicular lines are lines that intersect at a right angle (90 degrees).

Front

In a right triangle, what is the altitude to the hypotenuse?

Back

The altitude to the hypotenuse is the segment drawn from the right angle vertex to the hypotenuse, forming two smaller right triangles.

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 opposite side.

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.

Front

What is the difference between an altitude and a median?

Back

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

Front

Can an altitude be outside the triangle?

Back

Yes, in obtuse triangles, the altitude from the vertex opposite the obtuse angle falls outside the triangle.