Proving the Concurrency of Medians Theorem

This video tutorial explains how to prove the concurrency of medians theorem using parallel lines and properties of similar triangles. It begins with a review of midpoints, medians, and midsegments, followed by a discussion on parallel lines and angle-angle similarity. The tutorial then provides a step-by-step guide to proving the concurrency of medians, including a detailed two-column proof. The lesson concludes with a summary of the key concepts and a practical tip for understanding the centroid's properties.

What is the role of a median in a triangle?

• It is the longest side of the triangle.

• It connects a vertex to the midpoint of the opposite side.

• It divides the triangle into two equal areas.

• It is parallel to one side of the triangle.

What happens when parallel lines are cut by a transversal?

• The lines become equal in length.

• The lines intersect at a single point.

• Alternate interior angles are congruent.

• The lines become perpendicular.

How can you prove that two triangles are similar?

• By proving they have two congruent angles.

• By demonstrating they have equal areas.

• By showing they have the same number of sides.

• By showing they have the same perimeter.

What does the triangle midsegment theorem state about a midsegment?

• It is perpendicular to the side it is parallel to.

• It is twice the length of the side it is parallel to.

• It is equal in length to the side it is parallel to.

• It is half the length of the side it is parallel to.

In the proof of the concurrency of medians theorem, what is the significance of the point G?

• It is the endpoint of a median.

• It is the vertex of the triangle.

• It is the centroid where all medians intersect.

• It is the midpoint of the triangle.

What is the relationship between the segments DG and DB in the proof?

• DG is twice the length of DB.

• DG is one-third the length of DB.

• DG is equal to DB.

• DG is half the length of DB.

How does the centroid divide each median in a triangle?

• Into three equal parts.

• Into a 2:1 ratio, with the longer part towards the vertex.

• Into a 1:2 ratio, with the longer part towards the vertex.

• Into two equal parts.