Concept explainers
To find: The compare and contrast the perpendicular bisectors and
Answer to Problem 54HP
The perpendicular bisectors and angle bisectors of a triangle both are discussed.
Explanation of Solution
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)
A bisector bisects a segment, whereas an angle bisector bisects an angle.
Circumcenter theorem shows that the perpendicular bisector of the triangle intersects at a point called the circumcenter that is equidistance from the vertices of the triangle. Incenter theorem shows that the angle bisector of a triangle intersects at a point called the incenter that is equidistant from three sides of the triangle.
Inciter is always located inside a triangle.
Circumcircle is sometimes located inside a triangle.
If a triangle is acute, then the circumcenter is inside the triangle.
If a triangle is right, then the circumcenter is on the midpoint of the hypotenuse.
If a triangle is obtuse, then the circumcenter is outside the triangle.
Therefore, the perpendicular bisectors and angle bisectors of a triangle both are discussed.
Chapter 5 Solutions
Geometry, Student Edition
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