CK-12 Geometry - Second Edition

http://www.ck12.org Chapter 1. Basics of Geometry

Bis betweenAandCin this picture. As long asBisanywhere on the segment, it can be considered to bebetween
the endpoints.

Segment Addition Postulate:IfA,B, andCare collinear andBis betweenAandC, thenAB+BC=AC.

The picture above illustrates the Segment Addition Postulate. IfAB= 5 cmandBC= 12 cm, thenACmust equal
5 +12 or 17 cm. You may also think of this as the “sum of the partial lengths, will be equal to the whole length.”

Example 5:Make a sketch ofOP, whereQis betweenOandP.

Solution:DrawOPfirst, then placeQsomewhere along the segment.

Example 6:In the picture from Example 5, ifOP=17 andQP=6, what isOQ?

Solution: Use the Segment Additional Postulate. OQ+QP=OP, soOQ+ 6 =17, orOQ= 17 − 6 =11. So,
OQ=11.

Example 7: Make a sketch that matches the description:Sis betweenTandV. Ris betweenSandT. T R=
6 cm,RV= 23 cm,andT R=SV. Then, findSV,T S,RSandT V.

Solution:Interpret the first sentence first:Sis betweenTandV.

Then add in what we know aboutR: It is betweenSandT.

TofindSV, we know it is equal toT R, soSV= 6 cm.

For RS:RV=RS+SV For T S:T S=T R+RS For T V:T V=T R+RS+SV

23 =RS+ 6 T S= 6 + 17 T V= 6 + 17 + 6

RS= 17 cm T S= 23 cm T V= 29 cm

Example 8:Algebra ConnectionForHK, suppose thatJis betweenHandK. IfHJ= 2 x+ 4 ,JK= 3 x+ 3 ,and
KH=22, find the lengths ofHJandJK.

Solution:Use the Segment Addition Postulate and then substitute what we know.

HJ + JK =KH

( 2 x+ 4 )+( 3 x+ 3 ) = 22

5 x+ 7 = 22 So, ifx= 3 ,thenHJ=10 andJK= 12.

5 x= 15

x= 3