http://www.ck12.org Chapter 1. Basics of Geometry
Guided Practice
- DrawCD, such thatCD= 3. 825 in.
- IfOP=17 andQP=6, what isOQ?
- 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. - ForHK, suppose thatJis betweenHandK. IfHJ= 2 x+ 4 ,JK= 3 x+ 3 ,andKH=22, find the lengths ofHJ
andJK. - What is the distance between the two points shown below?
Answers:
1.To draw a line segment, start at “0” and draw a segment to 3.825 in. Put points at each end and label.
- Use the Segment Additional Postulate.OQ+QP=OP, soOQ+ 6 =17, orOQ= 17 − 6 =9. So,OQ=9.
- Interpret the first sentence first:Sis betweenTandV.
Then add in what we know aboutR: It is betweenSandT.
SV, 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- 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- Because this line is horizontal, look at the change in thex−coordinates.
|(− 4 )− 3 |=|− 7 |= 7
The distance between the two points is 7 units.
Practice
For 1-4, use the ruler in each picture to determine the length of the line segment.