1. 1. If p  q is the conditional, then its converse is ?. a. q  pb. ~q  pc. ~q  ~pd. q  ~p 2. Which statement is always true? a. x = xb. x = 2c. x = yd. x ≠ 0

2. 1. 6 2. 15 3. Never; 3 noncollinear points determine a plane 4. Always; through any two points there is exactly one line 5. Always; a plane contains at least three points not on the same line, and each pair of these determines a line 6. Postulate 2.1: through any two points, there is exactly one line. 7. Postulate 2.2; through any three points not on the same line, there is exactly one plane

4. Wednesday, October 26

5.  Students will be able to … ◦ identify properties of equality for real numbers ◦ determine which property justifies mathematical statements  Homework ◦ 2.6 pg 97-98 (14-23)

6. Write in the margin these in the margin Make sure to leave yourself enough room between each property to take notes Properties of Equality for Real Numbers properties that allow you to perform algebraic operations Reflexive Property Symmetric Property Transitive Property Addition and Subtraction Properties Multiplication and Division Properties Substitution Property Distributive Property

7.  For every number a a = a  Examples: ◦ 2 = 2 ◦ 0 = 0 ◦ x = x ◦ -y = -y

8.  For all numbers a and b if a = b, then b = a  Examples ◦ if x = y, then y = x ◦ if r + s = 2, then 2 = r + s ◦ if 3x – 5 = 1, then 1 = 3x - 5

9.  For all numbers a, b, and c if a = b and b = c, then a = c  Example ◦ if x + 2 = y and y = 7, then x + 2 = 7

10.  For all numbers a, b, and c if a = b, then a + c = b + c and a – c = b – c  Example ◦ if g = h, then g + 2 = h + 2

11.  For all numbers a, b, and c if a = b, then a * c = b * c and if c≠0, then (a/c) = (b/c)  For the division property, why must c≠0 in order for it to be true?

12.  For all numbers a and b if a = b, then a may be replaced by b in any equation or expression  Examples ◦ x = y and 5 + x = 17, then 5 + y = 17 ◦ r = s – 3 and 8 – r = 10, then 8 – (s – 3) = 10

13.  For all numbers a, b, and c a(b + c) = ab + ac  Example ◦ x(y – 4) = xy – 4x ◦ (u + v)9 = 9u + 9v

14. StepsReasons  Decide which property justifies each step  3(x-2) = 42  3x – 6 = 42  3x – 6 + 6 = 42 + 6  3x = 48  (3x)/3 = 48/3  x = 16  Original Equation  Distributive Property  Addition Property  Substitution Property  Division Property  Substitution

15.  You just proved that if 3(x – 2) = 42, then x = 16  Tomorrow we will create more proofs!

16.  2.6 pg 97-98 (14-23)

17.  What is one thing you learned today?  What is one question you still have?