Table of Contents
- 1 Is it true that the midpoint of a segment is equidistant from the endpoints?
- 2 What do you call is the set of all points equidistant from the endpoints of a segment?
- 3 Which of the following is the collection of points equidistant from the endpoints of a line segment *?
- 4 Which point is equidistant from the vertices?
- 5 How are points A and B equidistant from each other?
Is it true that the midpoint of a segment is equidistant from the endpoints?
IF a point is equidistant from the endpoint of a segment, then it must be the midpoint of the segment.
What is a point that is equidistant from the endpoint of the segment?
Vocabulary Language: English ▼ English
| Term | Definition |
|---|---|
| Perpendicular Bisector Theorem Converse | If a point is equidistant from the endpoints of a segment, then the point is on the perpendicular bisector of the segment. |
What is a point equidistant from the two end points of a line segment?
A point is said to be equidistant from two other points when it is at an equal distance away from both of them. For example, the perpendicular bisector of a line segment is equidistant from both endpoints.
What do you call is the set of all points equidistant from the endpoints of a segment?
circle
Definition: A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. We use the symbol ⊙ to represent a circle.
How can you determine if a point is equidistant from the sides of an angle?
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment. If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.
What is a line segment ray or plane that intersects the segment at its midpoint?
In chapter 1 we learned that a segment bisector intersects a segment at its midpoint. A segment, ray, line, or plane that is perpendicular to a segment at it’s midpoint is called a Perpendicular Bisector.
Which of the following is the collection of points equidistant from the endpoints of a line segment *?
Equivalently, the locus of all point equidistant from the endpoints of a segment is the perpendicular bisector of the segment. If each of two points is equidistant from the endpoints of a segment, then the line through these points is the perpendicular bisector of the segment.
How do you prove a point is equidistant from a line?
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 are equidistant points?
A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal. In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector.
Which point is equidistant from the vertices?
The circumcenter of a triangle
The circumcenter of a triangle is a point that is equidistant from all three vertices. The circumscribed circle is a circle whose center is the circumcenter and whose circumference passes through all three vertices. In order to construct the circumscribed circle, first find the circumcenter of a given triangle.
Is the point equidistant from the points on the edge?
Answer: The center of a circle is the point equidistant from the points on the edge.
Is a set of points that are equidistant from a line and a fixed point?
A parabola is the set of points equidistant from a line, called the directrix, and a fixed point, called the focus. A parabola is a set of points that are equidistant from a given line, which we call the directrix, and a given fixed point not on the line, called the focus.
The point that is equidistant from the two endpoints of the segment of a straight line is the midpoint of the segment. OR consider the perpendicular bisector of the segment, on both sides of the line. All points along this perpendicular bisector of the segment will be equidistant from the two endpoints of the segment.
How are points A and B equidistant from each other?
Both points A and B are from the midpoint which confirms that the midpoint is equidistant to points A and B. The concept of equidistance is used throughout geometry. Below are just a few examples. Parallel lines are equidistant from each other; any point on one line is always equal in distance from the other line.
Are there parallel lines that are equidistant from each other?
Like parallel lines, parallel planes are also equidistant from each other. Any point on one plane is equal in distance from the other plane. Any point on the perpendicular bisector of a line segment is equidistant from the segment’s endpoints.
When do you use the midpoint formula for a line segment?
The midpoint formula for this line segment will be: Two or more objects or points are said to be equidistant if they are at the same distance from a place. A midpoint is also equidistant from the two original points. We can use either the midpoint formula or the distance formula to show that a point is equidistant from the two given points.