Perpendicular bisector theorem

Front

What is the Perpendicular Bisector Theorem?

Back

The Perpendicular Bisector Theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

Front

If AF = 10x - 3 and FC = 8x + 3, what is AC?

Back

AC = AF + FC = (10x - 3) + (8x + 3) = 18x.

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

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

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; their intersection is the circumcenter.

Front

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

Back

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

Front

If GC = 11, what is AG if G is the midpoint of AC?

Back

AG = 11, since G is the midpoint.

Front

What segments intersect at the circumcenter?

Back

The segments that intersect at the circumcenter are the perpendicular bisectors of the sides of the triangle.

Front

What is the significance of the circumcenter in a triangle?

Back

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

Front

If OB = 6, what does this imply about point O?

Back

Point O is the circumcenter, and it is 6 units away from vertex B.