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Geometry 5-7 Complete Lesson: Inequalities in Two Triangles

By Matthew Richardson
Last updated over 3 years ago
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.

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. 3:00
  2. 1:30
  3. 1:00
  4. 5:00
  5. 12:20
  6. 8:30

Problem 1 Got It? What inequality relates LN and OQ in the figure?

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 ?

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?

Problem 2 Got It? How does the Hinge Theorem apply to this scenario?

Problem 3 Got It?

Problem 4 Got It? Complete the proof on the canvas.

Error Analysis: From the figure, your friend concludes that m∠BAD > m∠BCD. How would you correct your friend's mistake?

Compare and Contrast: How are the Hinge Theorem and the SAS Congruence Postualte similar? How are they different?

Review Lesson 5-6: Order the angles of the triangle from smallest to largest.

  1. ∠F
  2. ∠R
  3. ∠T

Review Lesson 5-6: Order the angles of the triangle from smallest to largest.

  1. ∠M
  2. ∠L
  3. ∠K

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.

Review Lesson 5-6: In △GHI, which side is included between ∠G and ∠H ?

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)

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.

Reflection: Math Success