Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

Can the lengths 101, 212, and 313 form a triangle?

Back

No, because 101 + 212 is not greater than 313.

Front

What is a centroid in 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 G is the centroid of triangle ABC and GF = 4, what is the length of GC?

Back

GC = 8, because the centroid divides each median in a 2:1 ratio.

Front

What is the relationship between the segments created by the centroid on a median?

Back

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

Front

If BE = 15, what is EG if G is the centroid?

Back

EG = 5, because the centroid divides BE in a 2:1 ratio.

Front

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

Back

CE = 16, as the centroid divides AC in a 2:1 ratio.

Front

If AG = 16, what is the length of GD?

Back

GD = 8, since the centroid divides the median in a 2:1 ratio.

Front

What is the formula for finding the length of a segment in a triangle when given the centroid?

Back

If AG is the length from a vertex to the centroid, then GD = AG/2.

Front

What does it mean if a set of lengths cannot form a triangle?

Back

It means that the lengths do not satisfy the Triangle Inequality Theorem.