CK-12 Geometry - Second Edition

http://www.ck12.org Chapter 2. Reasoning and Proof

Review Questions

For questions 1-8, solve each equation and justify each step.

1. 3x+ 11 =− 16


2. 7x− 3 = 3 x− 35
   3.^23 g+ 1 = 19
   4.^12 MN= 5


3. 5m^6 ABC= 540 ◦


4. 10b− 2 (b+ 3 ) = 5 b
   7.^14 y+^56 =^13
   8.^14 AB+^13 AB= 12 +^12 AB

For questions 9-14, use the given property or properties of equality to fill in the blank.x,y, andzare real numbers.

9. Symmetric: Ifx=3, then _____.


10. Distributive: If 4( 3 x− 8 ), then _____.


11. Transitive: Ify=12 andx=y, then _____.


12. Symmetric: Ifx+y=y+z, then _____.


13. Transitive: IfAB=5 andAB=CD, then _____.


14. Substitution: Ifx=y−7 andx=z+4, then _____.


15. Given pointsE,F, andGandEF=16,F G=7 andEG=23. Determine ifE,FandGare collinear.


16. Given pointsH,IandJandHI= 9 ,IJ=9 andHJ=16. Are the three points collinear? IsIthe midpoint?


17. Ifm^6 KLM= 56 ◦andm^6 KLM+m^6 NOP= 180 ◦, explain how^6 NOPmust be an obtuse angle.

Fill in the blanks in the proofs below.

18.Given:^6 ABC∼=DEF

(^6) GHI∼= (^6) JKLProve:m (^6) ABC+m (^6) GHI=m (^6) DEF+m (^6) JKL
TABLE2.18:
Statement Reason

1. Given
   2.m^6 ABC=m^6 DEF
   m^6 GHI=m^6 JKL


2. Addition PoE
   4.m^6 ABC+m^6 GHI=m^6 DEF+m^6 JKL

19.Given:Mis the midpoint ofAN.Nis the midpointMBProve:AM=NB

TABLE2.19:

Statement Reason

1. Given


2. Definition of a midpoint
   3.AM=NB