Centers of Triangles - Practice

Front

What is an angle bisector?

Back

An angle bisector is a line or segment that divides an angle into two equal parts.

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

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 a centroid?

Back

The centroid is the point where the three medians of a triangle intersect, and it is also the triangle's center of mass.

Front

If G is the centroid of triangle ABC, what is the relationship between the segments AG, GB, and GC?

Back

The segments AG, GB, and GC are in a 2:1 ratio, with AG being twice the length of GB and GC.

Front

What is a midsegment in a triangle?

Back

A midsegment is a segment that connects the midpoints of two sides of a triangle.

Front

How do you find the length of a segment when given the centroid?

Back

To find the length of a segment from the centroid to a vertex, multiply the length of the segment from the centroid to the midpoint of the opposite side by 3.

Front

What is the formula for finding 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, b, and c are the lengths of the sides of the triangle.

Front

What is the significance of the centroid in triangle geometry?

Back

The centroid is significant because it is the balance point of the triangle and divides each median into a 2:1 ratio.

Front

What are altitudes in a triangle?

Back

Altitudes are perpendicular segments from a vertex to the line containing the opposite side.