Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect, and it is equidistant from all three sides of the triangle.

Front

Why do you construct the angle bisectors to find the incenter?

Back

The intersections of angle bisectors are equidistant from the sides of the triangle.

Front

What is the formula to find the centroid of a triangle given its vertices?

Back

The centroid (M) can be found using the formula M = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3) for vertices (x1, y1), (x2, y2), (x3, y3).

Front

What is the location of the centroid in a scalene triangle?

Back

The centroid will always be inside the scalene triangle, since the centroid is always inside any type of triangle.

Front

What is a scalene triangle?

Back

A scalene triangle is a triangle with all sides of different lengths.

Front

What is the relationship between the centroid and the type of triangle?

Back

The centroid will be inside, on, or outside the triangle depending on whether it is acute, right, or obtuse.

Front

What does the inequality 2 < x < 12 represent?

Back

It represents that x can take any value greater than 2 and less than 12.

Front

In triangle ABC, if CJ = 18 and CG = BG, what is KJ?

Back

KJ = 6.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the point where the three medians of the triangle intersect and it divides each median into a ratio of 2:1.

Front

What is a median in a triangle?

Back

A median is a line segment from a vertex to the midpoint of the opposite side.