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

Define 'perpendicular bisector'.

Back

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

Front

If BC = 18, what is DC?

Back

DC = 9 (since the perpendicular bisector divides BC into two equal segments).

Front

Find BC if AD = 8 and AC = 24.

Back

BC = 24 (since AD is a segment of AC).

Front

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

Back

AC = 54 (by solving the equation AF + FC = AC).

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, and it is equidistant from the vertices of the triangle.

Front

If point O is the circumcenter of triangle ABC, and OB = 6, what can be inferred about OA and OC?

Back

OA and OC are also equal to 6, as the circumcenter is equidistant from all vertices.

Front

What is the relationship between the lengths of segments created by a perpendicular bisector?

Back

The segments created by a perpendicular bisector are equal in length.

Front

If a point lies on the perpendicular bisector of a segment, what can be said about its distance to the endpoints of the segment?

Back

The distances to the endpoints of the segment are equal.

Front

How do you find the length of a segment using the Perpendicular Bisector Theorem?

Back

You can use the theorem to set up equations based on the distances from a point on the bisector to the endpoints.