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MA.912.G.4.7 The Inequality Theorems

What You Need To Know...

The inequality theorems.

  1. The benchmark will be assessed using MC (Multiple Choice) items.
  2. Items may require the use of the triangle inequality, inequality in one triangle, or the Hinge Theorems.
  3. Items may be set in either mathematical or real-world contexts.

Example One

A surveyor took some measurements across a river, as shown below.  In the diagram, AC = DF and  AB = DE.


The surveyor determined that m∠ BAC = 29° and    m∠ EDF = 32°.  Which of the following can he conclude ?

  1. BC > EF
  2. BC < EF
  3. AC > DE
  4. AC < DF


Example Two

Kristin has two dogs, Buddy and Socks.  She stands at point K in the diagram and throws two disks.  Buddy catches one at point B, which is 11 meters (m) from Kristin.  Socks catches the other at point S, which is 6 m from Kristin.



If KSB forms a triangle, which could be the length, in meters, of segment SB?

  1.   5 m
  2.   8 m
  3. 17 m
  4. 22 m


Additional Examples



Triangle Inequality Theorem

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Hinge Theorem

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Reference Sheet