All Calendars Athletic District Calendar Events School Calendar 2017-2018 Graduation Dates 2017-2018 School Calendar 2018-2019 School Calendar 2019-2020 School Calendar 2020-2021 School Calendar 2021-2022 School Calendar 2022-2023 Uniform Statewide Assessment Calendar Work Calendar
Contacts Directory Accounting Operations Affirmative Action Alternative Education Athletics Behavior Education Support Team (BEST) Budgeting Certification Community Involvement Office Continuous Improvement Court Liaison Curriculum and Instruction Driver's Education Elementary Education Energy Management English Language Arts Escambia County Public Schools Foundation ESOL Evaluation Services Exceptional Student Education Facilities Planning FDLRS Finance and Business Services Fine Arts FOCUS Student Information System Food Services General Counsel Guidance Services Health Services High School Education Human Resource Services Information Technology Internal Auditing Maintenance and Custodial Services Math MediaServices Middle School Education New Facility Name Submissions Operations Payroll & Benefits Accounting PBIS Physical Education Professional Learning Protection Services Psychological Services Public Relations Purchasing Department Risk Management & Benefits Roy Hyatt Environmental Center SAZAC School Choice School Records School Social Workers Science_ECSD Social Studies Student Services Title I Transportation Warehouse Wellness Workforce Education Teaching Employment Opportunities Department Sub Folder Staff Forms
School Listing Page Elementary Schools Middle Schools High Schools Alternative Schools Virtual Academy School Listing with Contact Info Bus Transportation Info Enroll in a School Find Your School
School Board
AeSOP Board Meeting Information Bus Transportation Committees ECSD Meeting Info GroupWise Email Employee Pay Stub - Skyward Employment Information Financial Information Find Your School Focus Free & Reduced Meal Application Meal Payments My Links Risk Management & Benefits School Choice Information School Violence Staff Students Student of the Month Vendors Student Online Registration Teacher Resources Page TrueNorthLogic

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

This text will be replaced

Hinge Theorem

This text will be replaced

Reference Sheet