5.2 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

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 median, and c is the length of the side opposite the median.

Front

If FT = 3x + 8 and TE = 7x - 16, and GT is the median, how do you find x?

Back

Set FT equal to TE: 3x + 8 = 7x - 16, then solve for x.

Front

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

Back

A median divides the triangle into two smaller triangles of equal area.

Front

If CF, BE, and AD are medians of a triangle, what can be said about their intersection?

Back

The 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 also the center of mass of the triangle.

Front

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

Back

AF is also 10, since the median divides the opposite side into two equal segments.

Front

Which segment represents a median in a triangle?

Back

A median connects a vertex to the midpoint of the opposite side.

Front

What is the formula for the area of a triangle using medians?

Back

Area = (4/3) * (1/2) * m1 * m2 * sin(θ), where m1 and m2 are the lengths of two medians and θ is the angle between them.

Front

How do you determine if a segment is a median?

Back

A segment is a median if it connects a vertex of the triangle to the midpoint of the opposite side.