Standard

Derive the equation of a circle of given center and radius using the Pythagorean Theorem.

Thoughts

This should be a good next step to start tying together triangles and circles.

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.

Introduction

I am rereading George Polya’s excellent book How To Solve It: A New Aspect of Mathematical Method. I greatly enjoyed my first reading and it has had a profound impact on the way in which I teach. Some of the lessons from the books appear to common sense, but others are deeply impactful. I am hoping for inspiration. I frequently find myself faced with students who have all of the knowledge they need to complete a problem/assignment, but are paralyzed by indecision on starting the problems.