Medians and Altitudes (5.4)

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 a centroid?

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

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

If a median divides a triangle into two equal areas, what can be said about the segments it creates?

Back

The median divides the triangle into two triangles of equal area.

Front

In triangle ABC, if G is the centroid and AC = 32, what is the length of CE?

Back

CE = 16, since the centroid divides each median into a 2:1 ratio.

Front

If BF = 10 in triangle ABC, what is the length of AF if CF is a median?

Back

AF = 10, because the median divides the opposite side into two equal segments.

Front

In triangle XYZ, if YC = 15 and YB, XC, and ZA are medians, what is the length of YZ?

Back

YZ = 30, since the median divides the triangle into two equal areas.

Front

What is the relationship between the lengths of the segments created by a median?

Back

The lengths of the segments created by a median are equal on either side of the median.

Front

How do you find the length of a segment created by a median?

Back

To find the length of a segment created by a median, use the property that the median divides the opposite side into two equal lengths.