Students will be able to develop and prove hyptheses about angles in triangles, in preparation for the next lesson, in which they will develop a proof of the Pythagorean theorem.
Big Idea
Students work on proving hypotheses – and end up proving the Pythagorean Theorem.
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
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.
Look for and express regularity in repeated reasoning.
Introductory Problem
10 minutes
Proving Hypotheses
30 minutes
Closure
5 minutes
With about five minutes to go, I ask the students to stop working and I let them know that I’d like each group to report out on their progress with the Parallel Lines problem.
I ask to hear first from any groups who are not yet finished:
What is their hypothesis?
Where are they in the problem solving process?
Are they having any particular issues? If so, with what?
From groups who have finished, I ask for one observation from each group:
Did they struggle with anything in particular?
What did they find challenging?
Did they find these tasks difficult or easy, and why?