## Reflection: Vertical Alignment Algebraic Proof of the Perpendicular Bisector Theorem using Coordinate Geometry - Section 1: Activating Prior Knowledge

This unit on Analytic Geometry is valuable in at least two ways. For one, it allows students to appreciate the symbiotic relationship between algebra and geometry. On the other hand, it is provides a great transition to, and preparation for, the intermediate algebra courses that students will take the following year. So part of my job is to make sure that students have a good algebra foundation. If they don't, they will be so bogged down in the algebra that they'll see it as an added burden rather than as a powerful tool that aids in analyzing geometric relationships. They also won't be prepared for intermediate algebra.

One thing I realized in this lesson, is that my students had not committed the patterns for squaring binomials to memory. In other words, they were either squaring binomials by distributing and collecting like terms or else they were attempting to use shortcuts that led to wrong answers like (3x+4)^2 = 9x^2+16. So my message during this activating prior knowledge section was something like, "Students, you are getting to the point in your math career where you are expected to be more sophisticated and fluent with your algebra. When you get to Algebra 2 next year, your teacher will expect that you know (a+b)^2 is a^2+2ab+b^2, and you will be expected to handle anything with that structure, for example (3a - cosx)^2, quickly and accurately.

Because I knew that I wanted my students to be fluent in this skill, I spent a good amount of time practicing it during this Activating Prior Knowledge section. This paid off, too, as students had the skill down by the time we actually needed it in the next section of the lesson. This allowed them to focus on the geometry that was involved rather than being bogged down in the algebra we were using to analyze the geometry.

Making sure algebra foundations are good
Vertical Alignment: Making sure algebra foundations are good

# Algebraic Proof of the Perpendicular Bisector Theorem using Coordinate Geometry

Unit 9: Analytic Geometry
Lesson 2 of 7

## Big Idea: Feeling nostalgic? In this lesson students return to their Algebra roots in order to prove the perpendicular bisector theorem.

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60 minutes