5.1/5.2 practice CW Center of triangles

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 point where the three medians intersect and is located two-thirds of the distance from each vertex to the midpoint of the opposite side.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point of concurrency of the perpendicular bisectors of the sides of a triangle. It is equidistant from all three vertices of the triangle.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point of concurrency of the altitudes of a triangle. It can be located inside, on, or outside the triangle depending on the type of triangle.

Front

What is the incenter of a triangle?

Back

The incenter is the point of concurrency of the angle bisectors of a triangle. It is equidistant from all three sides of the triangle.

Front

If V is the centroid of triangle RST and SV = 6, what is the length of UV if UT = 7.5?

Back

UV = 3.

Front

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

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

How do you find the circumcenter of a triangle?

Back

To find the circumcenter, construct the perpendicular bisectors of at least two sides of the triangle. The point where they intersect is the circumcenter.

Front

How do you find the orthocenter of a triangle?

Back

To find the orthocenter, construct the altitudes from each vertex to the opposite side. The point where all three altitudes intersect is the orthocenter.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the center of mass of the triangle and is the point where the triangle balances perfectly.

Front

What is the formula for finding the length of a median in a triangle?

Back