5.4 DO NOW Midsegment, Circumcenter, Incenter Review

Front

What is the definition of a midsegment in a triangle?

Back

A midsegment is a segment that connects the midpoints of two sides of a triangle, and it is parallel to the third side.

Front

What is the relationship between the length of a midsegment and the length of the third side in a triangle?

Back

The length of the midsegment is half the length of the third side.

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.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle, making it the center of the circumcircle.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect.

Front

What is the significance of the incenter in a triangle?

Back

The incenter is equidistant from all three sides of the triangle, making it the center of the incircle.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect.

Front

What is the relationship between the centroid and the triangle's vertices?

Back

The centroid divides each median into a ratio of 2:1, with the longer segment being closer to the vertex.

Front

How do you find the length of a midsegment in triangle WUV if QR is the midsegment?

Back

The length of midsegment QR is half the length of side WU.

Front

What is the formula to find the circumradius (R) of a triangle?

Back

R = (abc) / (4K), where a, b, c are the lengths of the sides and K is the area of the triangle.