5-3: Segments in a Triangle

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is equidistant from the vertices of the triangle.

Front

What is the centroid of a triangle?

Back

The centroid is the point of concurrency of the medians of a triangle. It is the center of mass and divides each median into a ratio of 2:1.

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of the 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 perpendicular bisector?

Back

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

Front

What is a midsegment in a triangle?

Back

A midsegment is a segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and half its length.

Front

If BE = 15, what is EG if BE is divided in the ratio 3:1?

Back

EG = 5.

Front

If GC = 9, what is CF if GC is divided in the ratio 3:2?

Back

CF = 13.5.

Front

What is the relationship between the sides of a triangle and its medians?

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 side opposite the median.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the balance point of the triangle, where all three medians intersect.