1. B ELL -R INGER Write the converse of this statement. State whether the statement and its converse are true or false. If both are true, write a biconditional statement. IF both are false, write a counterexample. If DE+EF=DF, then points D, E, and F are collinear.

2. S ECTION 2.2: P ROPERTIES FROM A LGEBRA

3. P ROPERTIES FROM A LGEBRA Since the lengths of segments and the measure of angles are real numbers, a lot of the properties from algebra can be used in geometry. Here are some important properties from algebra that we will be using.

4. P ROPERTIES OF E QUALITY Addition Property: If a=b and c=d, then a+c=b+d Subtraction Property: If a=b and c=d, then a-c=b-d Multiplication Property: If a=b, then ca=cb Division Property: If a=b and c≠0, then Substitution Property: If a=b, then either a or b may be substituted for the other in any equation (or inequality)

5. P ROPERTIES OF E QUALITY C ONT ’ D Reflexive Property of equality or congruence: a=a or and Symmetric Property of equality or congruence : If a=b, then b=a or Ifthen Ifthen Transitive Property of equality or congruence : If a=b and b=c, then a=c If and then Distributive Property: a(b+c)=ab+ac

6. P ROPERTIES OF C ONGRUENCE Reflexive Property:and Symmetric Property: If then If then Transitive Property: If and then If and then

7. T RY S OME ! Justify Each statement with a property from algebra or a property of congruence 1. 2. If AB=CD and CD=EF, then AB=EF 3. If RS=TW, then TW=RS 4. If x+5=16, then x=11 5. If 5y=-20, then y=-4 6. If z/5=10, then z=50 7. 2(a+b)=2a+2b 8. If 2z-5=-3, then 2z=2 9. If 2x+y=70 and y=3x, then 2x+3x=70 10. If AB=CD, CD=EF and EF=23, then AB=23

8. S OLVE 3 X =6-1/2 X AND JUSTIFY EACH STEP Steps 1. 3x=6-1/2x 2. 6x=12-x 3. 7x=12 4. X=12/7 Reasons 1. Given 2. Multiplication Property of Equality 3. Addition Property of Equality 4. Division Property of Equality

9. G IVEN : RT AND PQ ARE INTERSECTING AT S SO THAT RS = PS AND ST = SQ P ROVE : RT = PQ Statements 1. RS=PS; ST=SQ 2. RS+ST=PS+SQ 3. RS+ST=RT; PS+SQ=PQ 4. RT=PQ Reasons 1. Given 2. Addition Prop. Of = 3. Segment Addition Postulate 4. Substitution Prop. R P Q S T

10. G IVEN : P ROVE : 12 3 O D CB A Statements 1. m<AOC=m<BOD 2. m<AOC=m<1+m<2m <BOD=m<2+m<3 3. m<1+m<2=m<2+m<3 4. m<2=m<2 5. m<1=m<3 Reasons 1. Given 2. Angle Addition Post. 3. Substitution Prop. 4. Reflexive Prop. 5. Subtraction Prop. of =

11. P RACTICE Do the Proofs Worksheet with a partner or group of 3. Do the Proofs Puzzle Alone!

12. H OMEWORK : Pg 41 #1-6