Geometry 5-6 Inequalities in One Triangle

by Matthew Richardson

| 24 QuestionsNote 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.

1

1

10 pts

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.

15 ft

12 ft

8 ft

5 ft

2 ft

2

2

10 pts

Problem 1 Got It? Why is m∠5 > m∠C?

3

3

10 pts

Problem 2 Got It?

A

B

C

4

4

10 pts

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

side SO

side OX

side XS

5

5

10 pts

Problem 4 Got It?

A

B

C

D

6

6

10 pts

Problem 4 Got It?

A

B

C

D

7

7

10 pts

Problem 5 Got It?

A

B

C

D

8

8

10 pts

A

B

C

9

9

10 pts

A

B

C

10

10

10 pts

A

B

C

D

12

10 pts

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

13

10 pts

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

The side is at least 2 ft long.

14

10 pts

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

△PQR has two congruent angles.

15

10 pts

Review Lesson 4-2: You know the following information.

By what theorem or postulate can you conclude that △ABC ≅ △XYZ ?

SAS

SSS

ASA

AAS

16

17

18

16

10 pts

Review Lesson 3-5: What is m∠P ?

Enter only a number.

17

10 pts

Review Lesson 3-5: What is m∠D ?

Enter only a number.

18

10 pts

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

Yes

No

19

70 pts

Vocabulary Review: Complete all 7 items on the canvas.

20

10 pts

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.

21

22

23

21

5 pts

XY

YZ

ZX

22

5 pts

XY

YZ

ZX

23

5 pts

XY

YZ

ZX

24

10 pts

Reflection: Math Success

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