Properties of Equality and Congruence

1. Properties of Equality and Congruence Objective #14 Homework #7

2. Reflexive Property Think of the Reflexive Property as a ‘reflection’ – when you look in the mirror, you see yourself.

3. Symmetric Property Think of the Symmetric Property as ‘symmetry’– whatever one equation says, the other must say the same to be symmetric.

4. Transitive Property Think of the Symmetric Property as ‘transit’– you are able to remove the “middle man” to connect the outer pieces.

5. 2.6 Properties

6. Example 1 If GH  JK, then JK  GH. a. SOLUTION b. Reflexive Property of Equality Name Properties of Equality and Congruence Name the property that the statement illustrates. b. DE = DE c. IfP  Q andQ  R, thenP  R. a. Symmetric Property of Congruence c. Transitive Property of Congruence

7. Checkpoint Name Properties of Equality and Congruence Name the property that the statement illustrates. 1. IfDF = FG and FG = GH, then DF = GH. 2. P  P Transitive Property of Equality Reflexive Property of Congruence ANSWER ANSWER 3. If mS mT, then mT mS. Symmetric Property of Equality ANSWER

8. Checkpoint Use Properties of Equality and Congruence 4. 1 and 2 are vertical angles, and 2  3. Show that 1  3. 1  2 Property of Congruence Theorem 2  3 Given _____ _____ ? ? 1  3 Vertical Angles; Transitive ANSWER

10. Justify each step used to solve for xGiven: 5X – 12 = 32 + X Statement 5X – 12 = 32 + X 5X = 44 + X 4X = 44 X = 11 Reason Given Addition Property Subtraction Property Division Property

11. Student example: Justify each step used to solve for x. Given: 7X + 12 = 4X - 15 Statement 7X + 12 = 4X – 15 7X = 4X – 27 3X = - 27 X = - 9 Reason Given Subtraction Property Subtraction Property Division Property

12. 5. In the diagram, M is the midpoint of AB. Show that AB =2· AM. Use Properties of Equality and Congruence Checkpoint Definition of MB = AM Postulate Property of Equality AB = AM + MB _____ _____ _____ ? ? ? AB = AM + AM AB = 2· AM Distributive property midpoint; Segment Addition; Substitution ANSWER

13. Statement 1. m ےAOC = 139 2. m ے AOB+m ےBOC=m ےAOC 3. X + (2X + 10) = 139 4. 3X + 10 = 139 5. 3X = 129 6. X = 43 Reason Given Angle Addition Postulate Substitution Property Simplify Subtraction Property Division Property Solve for x and justify each step B Given m ے AOC=139 A x 2x+10 C O

14. Example 3 SOLUTION m1+ m3=180° Definition of supplementary angles Justify the Congruent Supplements Theorem 1 and 2 are both supplementary to 3. Show that 1  2. m2+ m3=180° Definition of supplementary angles m1+ m3= m2+ m3 Substitution Property of Equality m1= m2 Subtraction Property of Equality 12 Definition of congruent angles