Points of ConCurrency

• ​A straight line that bisects the side of a triangle and is perpendicular to it

• bisect- cuts into two equal pieces

​​Perpendicular Bisector

• ​Where all 3 perpendicular bisectors intersect

• can be outside the triangle

• All vertices are equidistant from circumcenter

​​Circumcenter

Multiple Choice

Define: CIRCUMCENTER OF A TRAINGLE

• the intersection point of the three perpendicular bisectors of a triangle 
• when a circle passes through the three vertices of a triangle 
• the point of intersection of three or more lines 
• the intersection point of the three angle bisectors of a triangle 

Multiple Choice

The place where all three perpendicular bisectors meet is called the ...

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

What is the special property for circumcenters?

• The circumcenter is equally distant to the midpoint of the sides of the triangle.

• The circumcenter is equally distant to the vertices.

​A straight line that cuts through an angle of a triangle and is perpendicular to the opposite side.

Altitude

​Where all 3 altitudes intersect is called the orthocenter

Can be outside the triangle

​​Orthocenter

Multiple Choice

If D is the orthocenter, which type of line segments are drawn?

• Medians

• Altitudes

• Angle Bisectors

• Perpendicular Bisectors

Multiple Choice

The three altitudes of a triangle intersect at the_______________.

• circumcenter

• incenter

• centroid

• orthocenter

• An ANGLE BISECTOR is straight line that cuts an angle into two equal angles

• Where 3 angle bisectors intersect,

• is always inside

• incenter is EQUAL distance from all sides

​

​Incenter

Multiple Choice

Define: INCENTER OF A TRIANGLE

• the intersection point of the three angle bisectors of a triangle 
• when three or more lines intersect at a single point 
• the intersection point of the three perpendicular bisectors of a triangle 
• the point of intersection of three or more lines 

Multiple Choice

The INCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

Multiple Choice

What is the special property for incenters?

• The distance from the incenter to the sides will all be the same.

• The incenter is always outside the triangle.

Multiple Choice

1.  Point Z is the circumcenter of ΔRST. What is TZ?

• 3
• 5
• 4
• 6

• A line from each angle to the midpoint of the opposite side is called a MEDIAN

• Where all 3 medians intersect is called the CENTROID

• aka "center or mass or gravity"

• centroid is always inside the triangle

• divides the medians in a 2:1 ratio; the vertex to the centroid is 2/3 of the median.

Centroid

Multiple Choice

The CENTROID is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

Multiple Choice

Which center of a triangle is shown in the picture below?

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Choice

Which center of a triangle is shown in the picture below?

• Circumcenter

• Orthocenter

• Incenter

• Centroid

Multiple Select

Which types of centers are ALWAYS INSIDE the triangle? (Select all that apply)

• Orthocenter

• Incenter

• Centroid

• Circumcenter

Multiple Choice

What type of point of concurrency is pictured?

• Circumcenter

• Centroid

• Incenter

• Orthocenter

Multiple Choice

What type of special segments are being used?

• Perpendicular Bisectors

• Angle Bisectors

• Medians

• Altitudes