Medians/Altitudes

Front

What is an altitude in a triangle?

Back

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

Front

What is a median in a triangle?

Back

A median is a segment from a vertex of the triangle to the midpoint of the opposite side.

Front

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

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 vertex and c is the length of the opposite side.

Front

What is the relationship between the altitude and the area of a triangle?

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

If segment AH is an altitude, what does that imply about angle A?

Back

Angle A is a right angle (90 degrees) where segment AH meets the base.

Front

In triangle ABC, if BD is a median, what can be said about segments AD and DC?

Back

Segments AD and DC are equal in length.

Front

What is the significance of the centroid in relation to medians?

Back

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

Front

If QS is an altitude, how does it affect triangle PQR?

Back

It creates two right triangles, PQR and PQS, allowing for the use of trigonometric ratios.

Front

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

Back

Area = 1/2 * base * height, where height is the length of the altitude.