Front

What is a centroid in a triangle?

Back

The centroid is the point where the three medians of a triangle intersect. It is also the center of mass of the triangle.

Front

How do you find the length of a segment from the centroid to a vertex?

Back

The length from the centroid (G) to a vertex (e.g., A) is two-thirds the length of the median from that vertex to the midpoint of the opposite side.

Front

If G is the centroid of triangle ABC, and BE is a median, what is the relationship between BG and GE?

Back

BG is two-thirds of BE, and GE is one-third of BE.

Front

What is the formula for the area of a triangle?

Back

The area (A) of a triangle can be calculated using the formula: A = 1/2 * base * height.

Front

What does it mean for two angles to be congruent?

Back

Two angles are congruent if they have the same measure.

Front

What is the significance of the statement HA=HA in a proof?

Back

This statement represents the reflexive property of equality, which states that any quantity is equal to itself.

Front

How do you determine the length of a segment in a triangle given the centroid?

Back

To find the length of a segment from the centroid to a vertex, use the relationship that the segment from the centroid to the vertex is two-thirds the length of the median.

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

If CW = 30 in triangle XYZ, what is CX if X is the centroid?

Back

CX = 20, since the centroid divides the median in a 2:1 ratio.

Front

What is the relationship between the lengths of segments created by the centroid?

Back

The centroid divides each median into two segments, with the segment connecting the centroid to the vertex being twice as long as the segment connecting the centroid to the midpoint of the opposite side.