## What is the equidistance Theorem?

The Angle Bisector Equidistant Theorem state that any point that is on the angle bisector is an equal distance (“equidistant”) from the two sides of the angle. The converse of this is also true.

How do you prove equidistance?

You can use a point on a perpendicular bisector to prove that two segments are congruent. If the point is on the perpendicular bisector of a segment, then it’s equidistant from the endpoints of the segment.

What is the converse of the angle bisector theorem?

The converse of angle bisector theorem states that if the sides of a triangle satisfy the following condition “If a line drawn from a vertex of a triangle divides the opposite side into two parts such that they are proportional to the other two sides of the triangle”, it implies that the point on the opposite side of …

### What is equal distance?

Two objects are equidistant from a point if the distance between each object and that point are the same. If both you and your friend live a half mile from school, your houses are equidistant from school. Equidistant comes from the Late Latin aequidistantem, “equal distances,” by way of the French équidistant.

What is converse of the perpendicular bisector theorem?

The converse of the perpendicular bisector theorem states that if a point is equidistant from both the endpoints of the line segment in the same plane, then that point is on the perpendicular bisector of the line segment.

Can a ray be bisected?

Such a ray that divides an angle into two equal angles is called an angle bisector. Likewise, two rays that divide an angle into three congruent angles are called angle trisectors. Figure %: An angle bisected and trisected On the left, angle ABC is bisected by the ray BD.

## What are the 4 steps in constructing perpendicular bisector?

Step 1: Draw a line segment XY of any suitable length. Step 2: Take a compass, and with X as the center and with more than half of the line segment XY as width, draw arcs above and below the line segment. Step 3: Repeat the same step with Y as the center. Step 4: Label the points of intersection as ‘P’ and ‘Q’.