8.3 Medians and Altitudes of Triangles

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 measure of ∠HKG if HK is an altitude in ΔGHI?

Back

90°

Front

What is a centroid in a triangle?

Back

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

Front

If G is the centroid of triangle ABC and BE= 18, what is the length of BG?

Back

12

Front

If G is the centroid of triangle ABC and GF= 4, what is the length of GC?

Back

8

Front

What is a median in a triangle?

Back

A median is a line segment joining a vertex to the midpoint of the opposite side.

Front

If KL is a median in triangle ABC, what is the relationship between the lengths of AL and LC?

Back

AL = LC, since a median divides the opposite side into two equal segments.

Front

If GT is a median and FE is 16, what can be inferred about the lengths of segments created by the median?

Back

The median divides the opposite side into two equal segments.

Front

What is the formula to find 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 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 centroid in relation to the area of a triangle?

Back

The centroid divides the triangle into three smaller triangles of equal area.