Construction of Centers

Define: INCENTER OF A TRIANGLE

• the intersection point of the three angle bisectors of a triangle 

• the intersection point of the three perpendicular bisectors of a triangle 

The circumcenter of a triangle is equidistant from the _______ of the triangle.

• vertices

• sides

• midsegments

Joe owns businesses in Albany, Waycross, and Valdosta. He wants to set up an office that is the same distance to all three cities. Which center should he use to find the best location?

• centroid

• incenter

• circumcenter

Clare used a compass to make a circle with the radius the same length as segment AB. She labeled the center C. Which statement is true?

In the construction, A is the center of one circle, and B is the center of the other. Identify all segments that have the same length as segment AB.

The diagram was constructed with straightedge and compass tools. A is the center of one circle, and C is the center of the other. Select all line segments that must have the same length as segment AB

This diagram is a straightedge and compass construction. A is the center of one circle, and B, is the center of the other. Select all the true statements.

The diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other. Select all the true statements.

This diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other. Select ALL the true statements.

• AC = BC

• AC = BD

• CD = AB + AB

• ABD is an equilateral triangle

• ACBD is a square

If Z is the centroid, what type of segments are drawn?

• angle bisectors

• perpendicular bisectors

• altitudes

• medians