Big Ideas Math Geometry Chapter 6

What are perpendicular bisectors used for in triangles?

They are used to find measures and write equations for perpendicular bisectors.

What does it mean for a point to be equidistant from two figures?

It means the point is the same distance from each figure.

What does the Perpendicular Bisector Theorem state?

If a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

What is the Converse of the Perpendicular Bisector Theorem?

If a point is equidistant from the endpoints of a segment, then it lies on the perpendicular bisector of the segment.

What does the Angle Bisector Theorem state?

If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle.

What is the Converse of the Angle Bisector Theorem?

If a point is in the interior of an angle and is equidistant from the two sides of the angle, then it lies on the bisector of the angle.

Can the perpendicular bisector of a triangle pass through its vertices?

No, it never passes through vertices unless the triangle is isosceles or equilateral.

What concept involves using midpoints in triangles?

Lines, rays, and segments connect midpoints in triangles.

When writing the equation of a perpendicular bisector, what must be calculated?

The midpoint of the segment and the slope of the segment.

What is the significance of the equation related to perpendicular bisectors?

It provides the mathematical representation necessary to analyze geometric relationships within triangles.