http://www.ck12.org Chapter 2. Reasoning and Proof
Guided Practice
Use the given property or properties of equality to fill in the blank.x,y, andzare real numbers.
- Symmetric: Ifx=3, then __.
- Distributive: If 4( 3 x− 8 ), then __.
- Transitive: Ify=12 andx=y, then __.
Answers:
- 3=x
- 12x− 32
3.x= 12
Explore More
For questions 1-8, solve each equation and justify each step.
- 3x+ 11 =− 16
- 7x− 3 = 3 x− 35
3.^23 g+ 1 = 19
4.^12 MN= 5 - 5m^6 ABC= 540 ◦
- 10b− 2 (b+ 3 ) = 5 b
7.^14 y+^56 =^13
8.^14 AB+^13 AB= 12 +^12 AB
For questions 9-12, use the given property or properties of equality to fill in the blank.x,y, andzare real numbers.
- Symmetric: Ifx+y=y+z, then _____.
- Transitive: IfAB=5 andAB=CD, then _____.
- Substitution: Ifx=y−7 andx=z+4, then _____.
- Distributive: If 3( 2 x− 4 ) =y, then_____.
- Given pointsE,F, andGandEF=16,F G=7 andEG=23. Determine ifE,FandGare collinear.
- Given pointsH,IandJandHI= 9 ,IJ=9 andHJ=16. Are the three points collinear? IsIthe midpoint?
- Ifm^6 KLM= 56 ◦andm^6 KLM+m^6 NOP= 180 ◦, explain how^6 NOPmust be an obtuse angle.