Lesson Plan

Prove that the measures of the interior angles of a triangle sum to 180 degrees, using a construction involving a line parallel to one side through the opposite vertex

Prove that the base angles of an isosceles triangle are congruent, using either triangle congruence criteria or rigid motions (reflection)

Prove the Triangle Midsegment Theorem: the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length

Explain why the three medians of a triangle are concurrent and identify the centroid as the point that divides each median in a 2:1 ratio from vertex to midpoint

Apply these triangle theorems to solve geometric problems and construct further proofs

HSG.CO.C.10

HSG.CO.C.10: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; 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.