Centroid Properties in Triangles

This video tutorial explains the property of the centroid in a triangle, which divides each median into a 2:1 ratio. It begins with an introduction to the concept of medians and midpoints, followed by a detailed proof using the midpoint theorem. The video concludes with a summary of the property and its implications in geometry.

What is the ratio in which the centroid divides a median of a triangle?

• 1:2

• 2:1

• 1:1

• 3:1

What is a median in a triangle?

• A line that bisects an angle

• A line from the midpoint of one side to the midpoint of another side

• A line from a vertex to the midpoint of the opposite side

• A line from a vertex to the opposite side

What is the role of point P in the triangle?

• It is the midpoint of segment AC

• It is the midpoint of segment AB

• It is the midpoint of segment BC

• It is the centroid

What is the purpose of constructing perpendicular bisectors in the video?

• To find the centroid

• To find the midpoints of segments

• To find the orthocenter

• To find the circumcenter

What is the point called where all three medians of a triangle intersect?

• Circumcenter

• Centroid

• Incenter

• Orthocenter

In the proof, what is the significance of extending GR to point S?

• To bisect the angle at G

• To make GS equal to PG

• To find the midpoint of GR

• To create a new triangle

What theorem is applied to show that segment QG is parallel to segment CS?

• Pythagorean Theorem

• Angle Bisector Theorem

• Sine Rule

• Midpoint Theorem

Why is quadrilateral AGCS considered a parallelogram?

• It has parallel opposite sides

• It is inscribed in a circle

• It has equal angles

• It has equal sides

What property of a parallelogram is used to prove that segment GR is equal to segment RS?

• Opposite sides are equal

• Diagonals bisect each other

• Opposite angles are equal

• It is symmetrical

What is the significance of the segment GS in the proof?

• It is equal to segment GR

• It is unrelated to segment GR

• It is twice the length of segment GR

• It is half the length of segment GR