Chapter 5.1: Bisector of Triangles

Question 1

Perpendicular Bisector Theorem

Answer 1

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Example: If CD is a perpendicular bisector of AB, then AC=BC.

Question 2

Converse of Perpendicular Bisector Theorem:

Answer 2

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
Example: If AE=BE, then E lies on CD, the perpendicular bisector of AB.

Question 3

Perpendicular Bisector

Answer 3

a line, segment, or ray that passes through the midpoint of a side of a triangle and is perpendicular to that side

Question 4

Circumcenter Theorem

Answer 4

The perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle

Question 5

Angle Bisector Theorem

Answer 5

If a point is on the bisector of an angle, then it is equidistant from the sides of an angle

Question 6

Converse of the Angle Bisector Theorem

Answer 6

If a point in the interior of an angle is equidistant from the sides of a triangle, then it is on the bisector of the angle.

Question 7

Incenter Theorem

Answer 7

The angle bisectors of a triangle intersect at a point called the incenter that is equidistant from the sides of a triangle.

Question 8

Concurrent Lines

Answer 8

three or more lines that intersect at a common point

Question 9

Point of Concurrency

Answer 9

the point of intersection of concurrent lines

Question 10

Circumcenter

Answer 10

the point of concurrency of the perpendicular bisectors of a triangle

Question 11

Incenter

Answer 11

the point of concurrency of the angle bisectors of a triangle

Question 12

Angle Bisector

Answer 12

ray that divides angle into 2 congruent angles