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

If BC is 18, what is DC if D is the midpoint of BC?

Back

DC = 9, since D is the midpoint.

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

If point O is the circumcenter of triangle ABC, and OB = 6, what does this imply?

Back

It implies that point O is equidistant from vertices A, B, and C.

Front

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

Back

You can find the length of a segment by using the distances from the circumcenter to the endpoints.

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

If BC = 24, what is the length of segment AC if A is the midpoint of BC?

Back

AC = 12, since A is the midpoint.

Front

What does it mean for a line to be perpendicular to a segment?

Back

It means that the line intersects the segment at a 90-degree angle.