CHAPTER 9 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

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

What does it mean for a point to be equidistant from the vertices of a triangle?

Back

It means that the distance from that point to each vertex of the triangle is the same.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

If the circumcenter of triangle RST is point Z, what can be said about the distances from Z to R, S, and T?

Back

The distances from Z to R, S, and T are all equal.

Front

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

Back

The circumcenter is not necessarily equidistant from the sides of the triangle; it is equidistant from the vertices.

Front

How can you determine if a line segment is a perpendicular bisector?

Back

A line segment is a perpendicular bisector if it divides another segment into two equal lengths and forms right angles with that segment.

Front

What is the measure of angle A if angle B is 33 degrees and angle C is 67 degrees in triangle ABC?

Back

The measure of angle A is 180 - (33 + 67) = 80 degrees.

Front

In triangle XYZ, if the circumcenter is at point O and the distance from O to vertex X is 5, what is the distance from O to vertices Y and Z?

Back

The distance from O to vertices Y and Z is also 5, since the circumcenter is equidistant from all vertices.

Front

What is the significance of the circumcenter in triangle construction?

Back

The circumcenter is used to construct the circumcircle, which is the circle that passes through all three vertices of the triangle.