Exploring Perpendicular and Angle Bisectors

What is the first step in constructing the perpendicular bisector of a line segment?

• Draw a straight line through the midpoint.

• Draw arcs from both endpoints that intersect.

• Measure the length of the segment.

• Draw a circle with the midpoint as the center.

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

• It is at the midpoint of the segment.

• It is farther from one endpoint.

• It is equidistant from both endpoints.

• It is closer to one endpoint.

What does the converse of the perpendicular bisector theorem state?

• A point on the bisector is closer to one endpoint.

• A point equidistant from the endpoints lies on the bisector.

• A point equidistant from the endpoints is at the midpoint.

• A point on the bisector is at the midpoint.

What is the first step in constructing the bisector of an angle?

• Draw a circle with the vertex as the center.

• Measure the angle.

• Draw an arc that intersects both sides of the angle.

• Draw a straight line through the vertex.

What is true about a point on the angle bisector?

• It is at the midpoint of one side.

• It is at the vertex of the angle.

• It is equidistant from both sides of the angle.

• It is closer to one side of the angle.

How should the distance between a point and a line segment be measured?

• At any angle.

• Perpendicularly.

• Horizontally.

• Vertically.

What does the angle bisector theorem help determine?

• The measure of the angle.

• The midpoint of the angle.

• The length of the angle sides.

• The equidistant property of points from the angle sides.

What is necessary to confirm that a line segment is an angle bisector?

• The segment must be horizontal.

• The segment must be vertical.

• The segment must have congruence marks.

• The segment must be perpendicular to one side.

What can be concluded if a point is equidistant from the sides of an angle?

• The point lies on the angle bisector.

• The point is outside the angle.

• The point is at the vertex.

• The point is at the midpoint of one side.

What does the converse of the angle bisector theorem state?

• A point on the bisector is closer to one side.

• A point equidistant from the sides is at the midpoint.

• A point on the bisector is at the vertex.

• A point equidistant from the sides of an angle lies on the bisector.