Ohio Resource Center
Lessons
Discipline
Mathematics
9, 10, 11, 12
Professional Commentary

Students draw a triangle and the three medians of the triangle using Geometer's Sketchpad®. The students identify and measure the line segments between the vertices of the triangle and the centroid and between the centroid and the midpoints of the opposite sides using dynamic geometry software. They draw conclusions about the relationships among the lengths of those line segments, as well as relationships among the areas of the triangles formed. Activity sheets and suggestions for assessment are included. (author/sw/jk)

Common Core State Standards for Mathematics
Standards for Mathematical Practice
CCSS.Math.Practice.MP8
Look for and express regularity in repeated reasoning.
High School - Geometry
Congruence
Prove geometric theorems
HSG-CO.C.10
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Make geometric constructions
HSG-CO.D.12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.
Ohio Mathematics Academic Content Standards (2001)
Geometry and Spatial Sense Standard
Benchmarks (8–10)
E.
Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology.
H.
Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.