Centers of Triangles

Centers of Triangles

See what you can do! We'll review anything together!

Multiple Choice

The CENTROID is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

​What is a CENTROID?

​Medians will only BISECT each side.

​

​When they meet, you get the CENTROID.

Multiple Choice

The ORTHOCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

​What is an ORTHOCENTER?

​Altitudes are ONLY PERPENDICULAR.

​

​The altitudes are the HIEGHT of the triangle.

​

​They meet at the ORTHOCENTER.

Multiple Choice

The INCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

​What is an INCENTER?

​Each dashed line is an ANGLE BISECTOR. It only cuts the ANGLE.

​

​They all meet at the INCENTER.

​

​Notice: The circle is INside.

Multiple Choice

The CIRCUMCENTER is the intersection of which special segments?

• Angle Bisectors

• Perpendicular Bisectors

• Medians

• Altitudes

​What is a CIRCUMCENTER?

​This is created by the 3 perpendicular bisectors.

​

​Notice: Each vertex of the triangle is EQUIDISTANT from the circumcenter.

​

Why is that?! They are the RADIUS of the outside circle!

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 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 Choice

[Medians and Centroid]
If AC = 16, what is AM?

• 4
• 8
• 6
• 10

Multiple Choice

[Median and Centroid]
If AP = 12, what is AL?

• 6
• 12
• 18
• 24

Multiple Choice

[Angle Bisectors and Incenter]:
If PX is 5, what is PZ?

• 20
• 10
• 5
• 15

Multiple Choice

[Perpendicular Bisectors and Circumcenter]
If AF is 6, what is AC?

• 6
• 10
• 16
• 12

Multiple Choice

Find the value of x

• x=28
• x=14
• x=23
• x=46

Multiple Choice

Point O is the circumcenter of the triangle. Find OB

• OB = 4
• OB = 6
• OB = 5.1
• Not enough information

Multiple Choice

The centroid cuts each median into two segments.  The shorter segment is ___________ the length of the entire segment.

• one third
• two thirds
• three fourths
• one half

Poll

How do you feel about this topic?