Centroid and Midsegment Theorems in Triangles

Median

Segment from vertex to opposite side's midpoint.

Centroid

Intersection point of triangle's three medians.

Centroid Distance Conjecture

Centroid is double distance from vertex compared to midpoint.

Triangle Midsegment Theorem

Midsegment length is half of third side.

Midsegment

Segment joining midpoints of two triangle sides.

Vertex

Corner point of a triangle.

Opposite Side

Side directly across from a given vertex.

Midpoint

Point dividing a segment into two equal parts.

Volume 2, pg. 215

Reference for median definition in triangle.

Volume 2, pg. 216

Reference for centroid and distance conjecture.

Volume 2, pg. 217

Reference for guided instruction on centroids.

Volume 2, pg. 218

Reference for practice problems related to triangles.

Volume 2, pg. 222

Reference for midsegment theorem explanation.

Volume 2, pg. 223

Reference for midpoint and midsegment definitions.

Average of x-coordinates

Sum of x-coordinates divided by number of points.

Average of y-coordinates

Sum of y-coordinates divided by number of points.

Coordinates of Centroid

Calculated as averages of triangle vertices' coordinates.

Guided Practice

Exercises to reinforce understanding of triangle concepts.