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Intro to Coordinate Proofs

Intro to Coordinate Proofs

Daniel Oldakowski

on 20 January 2013

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Transcript of Intro to Coordinate Proofs

Introduction to Coordinate Proofs The Buildup to Coordinate Proofs The Coordinate Proof Toolbox Congratulations on completing this lesson!!! The Pythagorean Theorem In mathematics, when a statement is made, it cannot always be assumed to be true just because the teacher said it, or just because it "looks right". When we make a statement that we think is true , we need to prove it, we need to provide a proof. The proof we just worked through was a very simple example. Like all aspects of mathematics, proofs get more elaborate, more interesting, more complex, and more exciting. During the remainder of this lesson we will take a look at a certain type of proof, namely, coordinate proofs. But before we embark on our inspection of coordinate proofs, lets put together the tool box we will need to be successful. The Midpoint Formula The Distance Formula Pythagorean Theorem GP: p. 352 #2-4
IP: p. 353 #15-17 Midpoint Formula GP: p. 47 # 2-5
IP: p. 47 #12-17* p. 43 p. 348
p. 350 Distance Formula GP: p. 47 #8-10
IP: p. 48 #18,21,27 p. 44 GP: p. 352 #9,10,14
IP: p. 353 #22,26,27 only determine if the triangles are right triangles. Coordinate Proof p. 267 GP: p. 270 #2-7
IP: p. 271# 10,12,18,19,22-24 A proof is a logical argument used to justify the initial statement. Here is what that means to us: when asked to write a proof, we systematically lay out the steps we go through to reach our conclusion. This can include both mathematics and explanatory sentences. This may sound novel, but, you have been doing one kind of proof all throughout your algebra classes. Proof you've seen proofs before Proofs involve the math that you already know. All we ask is that you lay out the steps one by one and provide a reason for each step. Here is an example: Suppose we have the equation 5x=10. Can you solve for x? Now, let’s state the problem a little differently. Given: 5x=10.
Prove: x=2. The process is no different from how you would have answered the first question on this page, but we will write things out more precisely.
Let’s take a look. 3. Which we can simplify to x=2. And we are done. 1. We can start by dividing both sides by 5. 2. The equation becomes (5/5) x=10/5. That was an example of an algebraic proof. No problem! This problem looks different, but don't worry, you already know how to solve this one. Coordinate proofs are proofs done using coordinate geometry (the x-y plane) and algebra. Three of the most important tools you will need for coordinate proofs are listed below. Lets look at each one in more detail. Now that we have put together the tools we need to be successful at coordinate proofs, lets look at coordinate proofs in more detail. Ex. 1-4 *on problems #16 and 17 also find the midpoint of each segment and the length of the line that connects the midpoints of each pair of points. Conceptual Question: Pythagorean Theorem Explain how to use the Pythagorean Theorem to determine if a triangle is a right triangle. Conceptual Question: Distance Formula Explain how the distance formula can be used to show two line segments are congruent. Conceptual Question: Midpoint Formula If two line segments share the same midpoint does that mean they are congruent? Draw a diagram to support your answer. Ex. 1, 2 Ex. 3
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