Learning Goal
Part of: Prove geometric theorems — 2 of 3 cluster items
Prove theorems about triangles
**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.
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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.
What you'll learn
- 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
Slides
Interactive presentations perfect for visual learners • 2 slide decks
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback
Exercises
Practice problems to build fluency and understanding • 1 exercises