Geometry 5-7 Inequalities in Two Triangles
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by Matthew Richardson
| 19 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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1
20 pts
Solve It! Think of a clock or watch that has an hour hand and a minute hand. As minutes pass, the distance between the tip of the hour hand and the tip of the minute hand changes. This distance is x in the clock shown. Sort the times below from least to greatest length of x ?
  1. 12:20
  2. 8:30
  3. 3:00
  4. 1:00
  5. 1:30
  6. 5:00
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2
10 pts
Problem 1 Got It? What inequality relates LN and OQ in the figure?
LN > OQ
LN < OQ
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3
10 pts
Problem 1 Got It? Reasoning: In △ABC, AB = 3, BC = 4, and CA = 6. In △PQR, PQ = 3, QR = 5, and RP = 6. How can you use indirect reasoning to explain why m∠P > m∠A ?
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5 pts
Problem 2 Got It? The diagram shows a pair of scissors in two different positions. In which position is the distance between the tips of the two blades greater?
The distance between the tips of the two blades is greater in the figure on the left.
The distance between the tips of the two blades is greater in the figure on the right.
The distance between the tips of the two blades is equivalent in both figures.
5
10 pts
Problem 2 Got It? How does the Hinge Theorem apply to this scenario?
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10 pts
Problem 3 Got It?
A
B
C
D
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7
20 pts
Problem 4 Got It? Complete the proof on the canvas.
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8
10 pts
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B
C
D
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9
10 pts
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B
C
D
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11
10 pts
Error Analysis: From the figure, your friend concludes that m∠BAD > m∠BCD. How would you correct your friend's mistake?
12
10 pts
Compare and Contrast: How are the Hinge Theorem and the SAS Congruence Postualte similar? How are they different?
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10 pts
Review Lesson 5-6: Order the angles of the triangle from smallest to largest.
  1. ∠F
  2. ∠R
  3. ∠T
14
10 pts
Review Lesson 5-6: Order the angles of the triangle from smallest to largest.
  1. ∠L
  2. ∠M
  3. ∠K
15
10 pts
Review Lesson 5-6: Match the range of possible lengths for the third side of a triangle in the left column with the given lengths of two sides of a triangle in the right column.

Not all ranges will be used, only one per pair of side lengths.
  • 0 < x < 15
  • 0 < x < 6
  • 4 < x < 34
  • 5 < x < 11
  • 3< x < 6
  • 5 < x < 17
  • 15 cm, 19 cm
  • 6 ft, 11 ft
  • 3 in., 3 in.
16
10 pts
Review Lesson 5-6: In △GHI, which side is included between ∠G and ∠H ?
side GH
side HI
side IG
17
10 pts
Review Lesson 3-7: Match the slopes on the left with the pairs of points on the right.
  • -8/3
  • 3/4
  • 1
  • X(0, 6), Y(4, 9)
  • R(3, 8), S(6, 0)
  • A(4, 3), B(2, 1)
18
10 pts
Use Your Vocabulary: Identify which form of the word hinge is used in each sentence.
  • Noun
  • Verb
  • Everything hinges on his decision.
  • The hinge on the gate allows it to swing open or closed.
  • Your plan hinges on your teacher's approval.
  • The lid was attached to the jewelry box by two hinges.
19
10 pts
Reflection: Math Success
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