Geo31b
Standard 31b
Investigate, prove, and apply theorems about triangles, including but not limited to: the sum of the measures of the interior angles of a triangle is $180^{\circ}$; the base angles of isosceles triangles are congruent; the segment joining the midpoints of two sides of a triangle is parallel to the third side and half the length; a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem using triangle similarity.
Thoughts
We are using this standard as the introduction to triangles and then quadrilaterals and polygons. We have just completed the unit on parallel lines and transversal where we have proven angle congruences, the sum of the interior angles of a triangle is $\180^{circ}$ and the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles.
This should provide a firm foundation for jumping into the slightly more complex proofs involving triangles.