Geometry 5-6 Complete Lesson: Inequalities in One Triangle

By Matt Richardson

Last updated about 3 years ago

24 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.

Use the GeoGebra applet to explore possible (and impossible) triangle side length combinations.
Consider when three given side lengths can form a triangle and when they cannot.

HINT: The applet may also be useful for modeling and completing the Solve It! item that follows.

Solve It! For a neighborhood improvement project, you volunteer to help build a new sandbox at the town playground. You have two boards that will make up two sides of the triangular sandbox. Which boards can you use for the third side of the sandbox? Select all that apply.

Problem 1 Got It? Why is m∠5 > m∠C?

Problem 2 Got It?

Problem 3 Got It? Reasoning: In the figure, m∠S = 24 and m∠O = 130. Which side of △SOX is the shortest side?

Problem 4 Got It?

Problem 5 Got It?

Reasoning: Is it possible to draw a right triangle with an exterior angle measuring 88? Explain your reasoning.

Review Lesson 5-5: Write the first step of an indirect proof of the statement.

The side is at least 2 ft long.

Review Lesson 5-5: Write the first step of an indirect proof of the statement.

△PQR has two congruent angles.

Review Lesson 4-2: You know the following information.
By what theorem or postulate can you conclude that △ABC ≅ △XYZ ?

Review Lesson 3-5: What is m∠P ?
Enter only a number.

Review Lesson 3-5: What is m∠D ?
Enter only a number.

Review Lesson 3-5: Is it possible for AW to equal OG ?

Vocabulary Review: Complete all 7 items on the canvas.

Use Your Vocabulary: Complete each statement with the appropriate form of the word compare.

NOUN: comparison
VERB: compare

By __?__, a spider has more legs than a beetle.
You can __?__ products before deciding which to buy.
To __?__ quantities, you can write an equation or inequality.

Geometry 5-6 Complete Lesson: Inequalities in One Triangle

Solve It! For a neighborhood improvement project, you volunteer to help build a new sandbox at the town playground. You have two boards that will make up two sides of the triangular sandbox. Which boards can you use for the third side of the sandbox? Select all that apply.

Problem 1 Got It? Why is m∠5 > m∠C?

Problem 2 Got It?

Problem 3 Got It? Reasoning: In the figure, m∠S = 24 and m∠O = 130. Which side of △SOX is the shortest side?

Problem 4 Got It?

Problem 4 Got It?

Problem 5 Got It?

Reasoning: Is it possible to draw a right triangle with an exterior angle measuring 88? Explain your reasoning.

Review Lesson 5-5: Write the first step of an indirect proof of the statement.The side is at least 2 ft long.

Review Lesson 5-5: Write the first step of an indirect proof of the statement.△PQR has two congruent angles.

Review Lesson 4-2: You know the following information.By what theorem or postulate can you conclude that △ABC ≅ △XYZ ?

Review Lesson 3-5: What is m∠P ?Enter only a number.

Review Lesson 3-5: What is m∠D ?Enter only a number.

Review Lesson 3-5: Is it possible for AW to equal OG ?

Vocabulary Review: Complete all 7 items on the canvas.

Use Your Vocabulary: Complete each statement with the appropriate form of the word compare.

Reflection: Math Success

Review Lesson 5-5: Write the first step of an indirect proof of the statement.

The side is at least 2 ft long.

Review Lesson 5-5: Write the first step of an indirect proof of the statement.

△PQR has two congruent angles.

Review Lesson 4-2: You know the following information.
By what theorem or postulate can you conclude that △ABC ≅ △XYZ ?

Review Lesson 3-5: What is m∠P ?
Enter only a number.

Review Lesson 3-5: What is m∠D ?
Enter only a number.