5-2 Bisectors in Triangles

What is the definition of a perpendicular bisector of a triangle?

• A line that connects two vertices of the triangle

• A line that passes through the midpoint of a side of the triangle and is perpendicular to that side.

• A line that divides the triangle into two equal parts

• A line that is parallel to one of the sides of the triangle

How many perpendicular bisectors does a triangle have?

• 4

• 2

• 3

• 5

What is the definition of an angle bisector of a triangle?

• A line that divides an angle into two equal angles

• A line that divides an angle into three equal angles

• A line that divides a triangle into two equal parts

• A line that connects the midpoints of two sides of a triangle

In a triangle, if the angle bisectors are concurrent, what is the name of the point of concurrency?

• centroid

• orthocenter

• circumcenter

• incenter

In a triangle, if the perpendicular bisectors are concurrent, what is the name of the point of concurrency?

• centroid

• orthocenter

• circumcenter

• incenter

How can you use perpendicular bisectors to find the circumcenter of a triangle?

• By finding the point of intersection of the perpendicular bisectors of the sides of the triangle.

• By finding the midpoint of the sides of the triangle

• By finding the point of intersection of the medians of the triangle

• By finding the point of intersection of the altitudes of the triangle

Explain how to use angle bisectors to find the incenter of a triangle.

• Measure the angles of the triangle and find the average

• Connect the midpoints of the sides of the triangle

• Draw the perpendicular bisectors of the sides and find their intersection point

• Draw the angle bisectors of the triangle and find their intersection point

What conditions would be enough to prove that P is the circumcenter of △HJK? Select all that apply.

• △HJK is an acute triangle

What is the radius of the inscribed circle of △HJK?

• 2

• 6

• 10

• 22

What are the coordinates of the circumcenter of △ABC?