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

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

Back

To find the length of a segment using the Perpendicular Bisector Theorem, you can use the distances from a point on the bisector to the endpoints of the segment, which will be equal.

Front

What is a circumcenter in 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 D is the circumcenter of triangle ABC, what can be said about the distances from D to A, B, and C?

Back

The distances from D to A, B, and C are all equal, meaning DA = DB = DC.

Front

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

Back

The lengths of the segments created by a perpendicular bisector are equal; if a point lies on the bisector, it is equidistant from the endpoints of the segment.

Front

How can you use the Perpendicular Bisector Theorem to solve for unknown lengths in a triangle?

Back

You can set up equations based on the distances from a point on the bisector to the triangle's vertices and use the theorem to find unknown lengths.

Front

What is the significance of the point where the perpendicular bisector intersects a segment?

Back

The intersection point is the midpoint of the segment, and any point on the perpendicular bisector is equidistant from the segment's endpoints.

Front

How do you determine if a point is on the perpendicular bisector of a segment?

Back

A point is on the perpendicular bisector of a segment if it is equidistant from the endpoints of that segment.

Front

What is the formula for finding the midpoint of a segment?

Back

The midpoint M of a segment with endpoints A(x1, y1) and B(x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the definition of a bisector?

Back

A bisector is a line, segment, or ray that divides another segment into two equal parts.