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Geometry 5-6 Inequalities in One Triangle
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by Matthew Richardson
| 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.
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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.
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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
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2
10 pts
Problem 1 Got It? Why is m∠5 > mC?
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3
10 pts
Problem 2 Got It?
A
B
C
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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
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5
10 pts
Problem 4 Got It?
A
B
C
D
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6
10 pts
Problem 4 Got It?
A
B
C
D
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7
10 pts
Problem 5 Got It?
A
B
C
D
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8
10 pts
A
B
C
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9
10 pts
A
B
C
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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
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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.
• 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.
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21
5 pts
XY
YZ
ZX
22
5 pts
XY
YZ
ZX
23
5 pts
XY
YZ
ZX
24
10 pts
Reflection: Math Success