Do Now 5.5 Centers of Triangles review

Front

What is the circumcenter of a triangle?

Back

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

Front

If AC = 42, what is the length of DF if D is the midpoint of AC?

Back

DF = 21, since D is the midpoint, DF is half of AC.

Front

What is the centroid of a triangle?

Back

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

Front

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

Back

CE = 16, since the centroid divides the median in a 2:1 ratio.

Front

What is the relationship between the circumcenter and the vertices of a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle.

Front

How do you find the length of a segment in a triangle given the lengths of other segments?

Back

Use properties of triangle segments, such as the centroid dividing medians or the circumcenter's equidistance from vertices.

Front

What is the incenter of a triangle?

Back

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

Front

If point O is the circumcenter of triangle ABC, what can be said about the distances OA, OB, and OC?

Back

OA = OB = OC, as O is equidistant from all vertices.

Front

What is the significance of the centroid in a triangle?

Back

The centroid represents the center of mass and is the balance point of the triangle.

Front

If a triangle has sides of lengths 10, 24, and 26, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem (10^2 + 24^2 = 26^2).