Posted on

Geometry Ch5.1 #26-31

Question from Wyatt:

I am not understanding Chapter 5 lesson 1  problems 26-31.
Wyatt 

Answer from Dr. Callahan: 

Given the figure

 NewImage

And that you are GIVEN

AB < BC < CD < DE

  • #26 – AB < CD  and BC < DE
    This is true. Transitive
  • #27 – AB + BC  < CD  + DE 
    True. Addition Theorem of Inequality
  • #28 – AC < CE
    Could be rewritten as AB + BC < CD + DE.
    True. Addition
  • #29 – AD > DE
    Could be written as AB + BC + CD > DE
    False (Or we do not KNOW it is true). If AB = 1 inch, BC = 2 inch, CD = 3 inch, and DE = 3.1 inch this fits the given criteria but #29 will be false. So we are looking here for places where this is not ALWAYS true with what we are given. If not ALWAYS true, it is False. 
  • #30 – BD > BC
    Write as BC + CD > BC
    True. Addition
  • #31 – AB < BD
    AB < BC + CD
    True – Addition.