Understanding Triangle Centers

Which point is formed by the intersection of the perpendicular bisectors of a triangle?

• Incenter

• Centroid

• Circumcenter

• Orthocenter

What is the name of the point where the medians of a triangle intersect?

• Orthocenter

• Centroid

• Circumcenter

• Incenter

How is the centroid positioned in relation to the vertex and the opposite side of a triangle?

• Equidistant from all sides

• Two-thirds of the way from the vertex

• At the midpoint of the opposite side

• Halfway from the vertex

If the length from the vertex to the centroid is 8, what is the total length of the median?

• 20

• 16

• 24

• 12

What is the relationship between the smaller and larger segments of a median divided by the centroid?

• The larger segment is twice the smaller segment

• The smaller segment is three times the larger segment

• The smaller segment is twice the larger segment

• Both segments are equal

What is the orthocenter of a triangle?

• The point where perpendicular bisectors meet

• The point where altitudes meet

• The point where medians meet

• The point where angle bisectors meet

Which of the following is true about the orthocenter?

• It is always inside the triangle

• It has no special properties related to length

• It is equidistant from all vertices

• It is the center of gravity

What is the special property of the centroid in terms of balance?

• It is the midpoint of the longest side

• It is equidistant from all sides

• It is the center of gravity

• It is the midpoint of the shortest side

Which center of a triangle is used to balance it on a point?

• Incenter

• Orthocenter

• Centroid

• Circumcenter

What should you use to memorize the properties of triangle centers effectively?

• Videos

• Flashcards

• Diagrams

• Textbooks