Curriculum  /  Math  /  10th Grade  /  Unit 1: Constructions, Proof, and Rigid Motion  /  Lesson 6

Constructions, Proof, and Rigid Motion

Lesson 6

Math

Unit 1

10th Grade

Lesson 6 of 19

Objective

Use principles of proof to justify each step in solving an equation.

Common Core Standards

Core Standards

  • A.REI.A.1 — Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Foundational Standards

  • 8.EE.C.7

Criteria for Success

  1. Define a proof as a detailed explanation of a theorem using a series of logical statements and reasons for those statements that follow from other statements accepted as true.
  2. Define a theorem as a mathematical statement that has been proven.
  3. Use the transitive property to show that if a=b and b=c, then a=c. This property can also be thought of as similar to substitution.
  4. Justify algebraic statements using properties of operations and equality.

 

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Anchor Problems

25-30 minutes

Problem 1

Given:  $${2\left ( x+3 \right )-8=10}$$

Prove:  $${x=6}$$

Guiding Questions

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Problem 2

Given:  $${a=3x+6}$$ and $${x=\frac{1}{3}b-2}$$

Prove:  $${a=b}$$

Guiding Questions

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Problem 3

Given: $${f(x)=(a-b)(a+b)}$$, $${g(x)=a^2-b^2}$$

Prove: $${f(x) = g(x)}$$ for all values where $${a\neq 0}$$, $${b\neq 0}$$ and $${a\neq b}$$

Guiding Questions

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Target Task

5-10 minutes

Given: $${j(x) = (a+b)^2}$$, $${h(x) = a^2 + 2ab + b^2}$$

Prove: $${j(x) = h(x)}$$

Next

Use angle relationships around a point to find missing measures. Prove angle relationships around a point using geometric statements and reasons.

Lesson 7
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Lesson Map

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Topic A: Constructions of Basic Geometric Figures

Topic B: Justification and Proof of Angle Measure

Topic C: Translations of Points, Line Segments, and Angles, and Parallel Line Relationships

Topic D: Reflections and Rotations of Points, Line Segments, and Angles

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