5.7 Inequalities in Two Triangles

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5.7 Inequalities in Two Triangles

• The Hinge Theorem (SAS Inequality Theorem)
• If two sides of one triangle are congruent to two
  sides of another triangle, and the included
  angles are not congruent, then the longer third
  side is opposite the larger included angle.

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Using the Hinge Theorem

• Which of the following statements must be true?
• AS lt YU
• SK gt YU
• SK lt YU
• AK YU
• The answer is B. SK gt YU

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Converse of the Hinge Theorem (SSS Inequality)

• If two sides of one triangle are congruent to two
  sides of another triangle, and the third sides
  are not congruent, then the larger included angle
  is opposite the longer third side.

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Using the Converse of the Hinge Theorem

• What is the range of the possible values for x?

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Using the Converse of the Hinge Theorem

• Step 1 Find an upper limit for the value of x.
• RS gt TS
• 60 gt 5x 20
• 80 gt 5x
• 16 gt x
• Step 2 Find a lower limit for the value of x.
• 5x 20 gt 0
• 5x gt 20
• x gt 4
• So, 4 lt x lt 16.

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More Practice!!!!!

• Homework Textbook p. 336 - 337 1 14, 16
  18 ALL