To find: Whether the statement “the
Answer to Problem 50HP
The statement “the angle bisector of a triangle intersect at a point that is equidistance from the vertices of the triangle” is sometimes true.
Explanation of Solution
Given information:
The given statement is “the angle bisector of a triangle intersects at a point that is equidistance from the vertices of the triangle”.
Calculation:
The perpendicular bisector of the triangle intersects at a point called the circumcenter that is equidistance from the vertices of the triangle. (Circumcenter theorem)
The angle bisector of a triangle intersects at a point called the incenter that is equidistant from three sides of the triangle. (incenter theorem)
If the incenter and the circumcenter coincide, then the angle bisectors intersect at a point that is equidistant from the vertices of the triangle. In this case the triangle is regular.
If the incenter and the circumcenter do not coincide, then the angle bisectors do not intersect at a point that is equidistant from the vertices of the triangle. In this case the triangle is not regular.
So, the statement is sometimes true.
Therefore, the statement “the angle bisector of a triangle intersects at a point that is equidistance from the vertices of the triangle” is sometimes true.
Chapter 5 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
College Algebra (7th Edition)
Elementary Statistics (13th Edition)
Trigonometry (11th Edition)
Probability and Statistics for Engineers and Scientists
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning