October 10, 2014
Questions
October 10, 2014
Algebra Properties Used in Geometry
Postulates of Equality
For any real numbers a, b, and c:
Reflexive Property of Equality: a = a
Symmetric Property of Equality: If a = b, then b = a.
Transitive Property of Equality: If a = b and b = c, then a = c.
Postulates of Equality and Operations
For any real numbers a, b, and c:
Addition Property of Equality: If a = b, the a + b = b + c
Multiplication Property of Equality: If a = b, then ac = bc.
Postulates of Inequality and Operations
For any real numbers a, b, and c:
Transitive Property of Inequality: If a < b and b < c, then a < c.
Addition Property of Inequality: If a < b, then a + c < b + c
Multiplication Properties of Inequality: If a < b and c > 0, then ac < bc.
Postulates of Equality and Inequality
For any real numbers a, b, and c:
Equation to Inequality Property: If and b are positive numbers and
a + b = c, then c > a and c > b.
Substitution Property: If a = b, then a may be substituted for b in
any expression.
October 10, 2014
Examples
1. Name the properties of inequality and operations that are used
in solving 180 < 12m - 30.
2. Knowing that m X < m Y, what can you conclude about
m X + m Z and m Y + m Z using the Addition Property
of Inequality.
In 3-5, which postulates of algebra justifies the statement?
3. If A, B, and C are distinct points and AB + BC = 10, then
AB < 10 and BC < 10.
4. If BC < AB and AB < AC, then BC < AC.
5. PQ + QR = QR + PQ.
October 10, 2014
Assignment: p. 148 (1-17)