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Geometry Proofs: Build a Logical Argument: Givens, reasons, congruence, and similarity

Grades 9–12Level 4
Cover of Geometry Proofs: Build a Logical Argument: Givens, reasons, congruence, and similarity

About this book

State what you know, cite why it is true, then conclude.

A proof is a chain of statements, and every link needs a reason. This workbook helps learners in grades 9–12 build that chain one step at a time. It starts with givens, conditionals, converses, and counterexamples. It then uses vertical angles and parallel lines to build short angle proofs. Learners prove triangles congruent with SSS, SAS, ASA, AAS, and HL, then use AA similarity to find unknown lengths. Error-analysis pages show common mistakes, such as assuming lines are parallel or reasoning in a circle. An explanatory answer key helps adults check reasoning, not only final answers.

  • Readiness check with a clear starting route
  • Worked examples with every reason written out
  • Two-column and paragraph proofs, practiced step by step
  • Error analysis of converses, SSA, AAA, and circular proofs
  • Answer key with criteria, common errors, and reteach cues

For grades 9–12 learners who know angle facts, the Pythagorean theorem, and linear equations.

Look inside

Page 5 of Geometry Proofs: Build a Logical Argument. Step 2, Concept: Claims, givens, and reasons
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Page 6 of Geometry Proofs: Build a Logical Argument. Step 3, Worked Example: Claims, givens, and reasons
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What this book covers

Covered

  • In this book: givens, conclusions, conditionals, converses, and counterexamples (pp. 5–14); angle proofs with vertical angles and parallel lines (pp. 15–24); triangle congruence with SSS, SAS, ASA, AAS, and HL (pp. 25–34); AA similarity, side ratios, and proof revision (pp. 35–44).
  • Added pages prove three theorems: vertical angles, triangle angle sum, and perpendicular bisector (pp. 53–55).

Not covered

  • Not in this book: circle theorems, coordinate proofs, constructions, and trigonometry.
  • The Pythagorean theorem is used as a known fact.

Before you start

If equations feel shaky, first use Expressions and One-Variable Equations.

Notice

Pictures in this book are simplified learning models. Check answers with the explanations at the back of the book.

The steps in this book

How the steps work
  1. Step 1: Readiness Check

    Check the skills you need before you begin. If something feels tricky, an adult can help you start in the right place.

  2. Step 2: Concept

    Read a short, clear explanation of the new idea and the words that go with it.

  3. Step 3: Worked Example

    Watch the idea being used, one step at a time, in a worked example.

  4. Step 4: Guided Practice

    Practice with prompts and help cues. The help gets smaller as you get stronger.

  5. Step 5: Independent Practice

    Practice on your own with different kinds of questions, and explain your thinking.

  6. Step 6: Review

    Look back at earlier learning so it stays strong, then check where to go next.

  7. Step 7: Answers and Explanations

    Check your answers. Each answer explains why, names a common mistake, and shows how to fix it.

What is in the book

The modules

  1. Module 1: Claims, givens, and reasonsPages 5–14
  2. Module 2: Angle relationships form proof chainsPages 15–24
  3. Module 3: Congruent triangles justify equal partsPages 25–34
  4. Module 4: Similarity and proof revisionPages 35–44

Contents

  1. Readiness check, pp. 3–4. Before Module 1. Its table tells you where to start.
  2. Modules, pp. 5–44
  3. Checkpoints, pp. 14, 24, 34, 44. The last page of each module.
  4. Mixed review, pp. 45–48. Questions from across the book, mixed together.
  5. Exit check, pp. 49–50. A last check across the book.
  6. Reflect and repair, p. 51
  7. Try again, p. 52. Fresh questions like those in the exit check.
  8. Further practice, pp. 53–55. More pages of step 5, Independent Practice.
  9. Extra practice, pp. 56–57
  10. Answers and explanations, pp. 58–68. Notes in this part are headed “Why”, “Common mistake” and “Help”.

Before this book

If equations feel shaky, first use Expressions and One-Variable Equations.

After this book

For side-and-angle work next, see Right-Triangle Trigonometry.

Also mentioned

Argument Writing: Claims, Reasons, and Evidence builds the same habit in writing.

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