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Geometry 5-5 Complete Lesson: Indirect Proof

By Matt Richardson
Last updated about 3 years ago
18 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! The goal of this game is to fill in the empty squares with numbers. The numbers 1, 2, 3, and 4 must appear once in each row and once in each column. Complete the games on the canvas.

Problem 1 Got It?

Problem 1 Got It?

Problem 2 Got It? Which two statements contradict each other?

I. △XYZ is acute.
II. △XYZ is scalene.
III. △XYZ is equiangular.

Problem 2 Got It? Reasoning: Statements I and II below contradict each other. Statement III is the negation of Statement I. Are statements II and III equivalent?

I. △ABC is scalene.
II. △ABC is equilateral.
III. △ABC is not scalene.

Problem 3 Got It? Complete the proof on the canvas.

Given: 7(x + y) = 70 and x ≠ 4.
Prove: y ≠ 6.

Write a statement that contradicts the following statement. Draw a diagram to support your answer.

Lines a and b are parallel.

Error Analysis: A classmate began an indirect proof as shown below. Explain and correct your classmate's error.

Review Lesson 5-4: The distances from the centroid of a triangle to its vertices are 16 cm, 17 cm, and 18 cm. What is the length of the shortest median?

Review Lesson 5-4: The orthocenter of isosceles △ABC lies outside the triangle and m∠A = 30. What are the measures of the other two angles? Select all that apply.

Review Lesson 2-4: You think, "If I leave home at 7:10, I'll catch the 7:25 bus. If I catch the 7:25 bus, I'll get to school before class starts. I am leaving and it's 7:10, so I'll get to school on time." Which law of deductive reasoning are you using?

Review Lesson 1-7: Identify the shortest and longest sides of △ABC.

  • side AB
  • side BC
  • side AC
  • Shortest
  • Longest

Review Lesson 1-7: Identify the shortest and longest sides of △ABC.

  • side AB
  • side BC
  • side AC
  • Shortest
  • Longest

Vocabulary Review: Draw a line from each statement in Column A to one or more pictures that contradicts it in Column B.

Use Your Vocabulary: Write indirect or indirectly to complete the sentence.

The __?__ way home from school takes a lot more time.

Respond with one word, no spaces.

Use Your Vocabulary: Write indirect or indirectly to complete the sentence.

By finding the negation of a statement false, you __?__ prove the statement true.

Respond with one word, no spaces.

Reflection: Math Success