Geometry
This summer we will use this page to review topics that will be most important for the 2023-2024 school year in Geometry. We will begin with a review of some key concepts from Algebra 1 like graphing linear functions, the distance and midpoint formulas, and systems of equations. Later in the program we will begin to introduce some of the key pieces of geometry so we will be set to hit the ground running when we get back to school in the fall!
Module 1: Intercepts and Slope
In Module 1 we start taking a look at some of the basics of graphing linear functions. Mr. Ator goes over how to find x and y intercepts graphically then goes over what slope is and how to find it.
Module 2: Graphing Linear Functions
In Module 2 we are going to take a look at how to use two different formulas to graph linear functions. The first is slope-intercept form and the second is point-slope form.
Module 3: Equation of a line through a given Point
Previously we discussed how to graph a line given an equation. This time through we're going to work backwards and figure out how to write the equation of a line given the points using Slope-Intercept form and Point-Slope Form.
Module 4: Special lines (Horizontal, Vertical, Parallel, and Perpendicular)
In Geometry we will have occasion to work with parallel, perpendicular, horizontal and vertical lines. These concepts are so important are occur so often that we devote this module to describing them and learning how to write their equations.
Module 5: Solving a Linear Equation
Linear equations of the type generated when we are solving systems of equations are very common in Geometry. These are typically equations in one variable, e.g. x . How do we go about solving for x ? Generally, we aim to isolate the variable by performing the same algebraic operation on both sides of the equation (algebraic properties of equality), thus simplifying the equation until we get to a answer.
Module 6: Solving Systems of equations
with Substitution
with Substitution
Sometimes we are given two linear equations, and we are asked to determine the point (if any) where the lines described meet, i.e cross one another; we called this the intersection point. With substitution, you solve one of the equations for one of the variables, and then substitute that quantity into the remaining equation.
Module 7: Solving Systems of equations
with Elimination
with Elimination
Solving a system using linear elimination involves multiplying each equation by conveniently selected differing constants so that a variable will be eliminated when the equations are added or subtracted. Once a variable is eliminated, we solve for the remaining variable.
Module 8: Solving Systems of equations by Graphing
Solving a system by graphing involves plotting the lines on the Cartesian Plane using a calculator and using the Intersect feature to determine where (if at all) the lines have a common point, i.e. they cross (intersect) each other at that point.
Module 9: Solving a Proportion
What is a proportion? How to solve them efficiently and effectively.
Module 10 Simplifying Radicals
In this module we will take a look at methods for simplifying radicals. We call this Simplest Radical Form.