Geometry 5-5 Complete Lesson: Indirect Proof

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 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.

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.

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

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

Geometry 5-5 Complete Lesson: Indirect Proof

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.

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

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

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.

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.