Geometry Chapter 2 2 6 Properties of Equality

Geometry: Chapter 2 2. 6: Properties of Equality and Congruency Obj: Identify properties of equality and congruency

Examples of Properties

Properties of Equality and Congruency • Reflexive Property: • Equality _______________________ • Symmetric Property: Congruency _____________________________ • Equality ___________ Congruency _________________________ • Transitive Property: • Equality ___________________________ • • Congruency ____________________________ _______________

Practice: Name the property that the statement illustrates. 1) If GH = JK, then JK = GH. ______________ 2) DE = DE ______________ 3) If <P = <Q and <Q = <R, then <P = <R _________________

In the diagram <1 and <2 are a linear pair and m<1 = m<3. Fill in the reasons to show that m<2 +m<3 = 180 m<2 + m<1 = 180 m<1 = m<3 m<2 + m<3 = 180

Addition Property: Example: • Adding the same number to each side of an equation produces an equivalent equation Subtraction Property: Example: • Subtracting the same number to each side of an equation produces an equivalent equation

• Multiplication Property: Example: Multiplying the same number to each side of an equation by the same nonzero number produces an equivalent equation Division Property: Example: Dividing the same number to each side of an equation by the same nonzero Number produces an equivalent equation

• Substitution Prop: Example: • Substituting a number for a variable in an equation produces an equivalent equation.

• Practice: In the picture <1 and <2 are both supplementary to <3. Show that <1= <2 • m<1 + m<3 = 180 __________ • m<2 + m<3 = 180 __________ • m<1 + m<3 = m<2 + m<3 __________ • m<1 = m<2 __________ • <1 = <2 __________