STATE-ment of Affairs
What is a Conditional Statement?
A statement in the form of If p, then q. Where p is the Hypothesis, and q is the Conclusion
The first step in a proof is always what?
We start with a piece of given information
What are the Closure, Identity and Inverse Properties of Algebra (respectively). 100 Points for each correct answer.
Closure- Operations between real numbers results in a real number
Identity- a + 0 = 1, a*1 = a
Inverse- a + -a = 0, a * (1/a) = 1
If given a = b and c = d, describe:
-What the Addition Property of Equality state
-What the Subtraction Property of Equality state
100 Points for each correct answer.
a + c = b + d (Addition); a - c = b - d (Subtraction)
What is the Converse of a statement?
When the hypothesis and conclusion are flipped. Sample: If q, then p
What does the Midpoint Theorem state?
If M is the midpoint of Line Segment AB, then
AM = 1/2 AB and MB = 1/2 AB
What is the Commutative Property for Addition? Multiplication?
a + b = b + a (Addition), ab = ba (Multiplication)
If given a = b and c = d, describe:
-What the Multiplication Property of Equality state
-What the Division Property of Equality state
100 Points for each correct answer.
ac = bd (Multiplication); a/c = b/d (Division)
What is a Counterexample?
Bonus (+100) - What is a Counterexample to this statement: If CD + DE = CE, then CD = DE (Draw it on the board)
A statement that shows a conditional is false: the Hypothesis is true, but the Conclusion is false
Bonus (+100): Answers may vary; Draw a line segment where CD and DE are not marked as congruent
What does the Angle Bisector Theorem state?
If Ray BX is the bisector of Angle ABC, then the measure of angle ABX = 1/2 of the measure of angle ABC, and measure of angle XBC = 1/2 the measure of angle ABC
What are the Properties of Congruence? (These ones derive from Properties of Algebra) 100 Points for each correct answer.
Daily Double- Give an example of these each of these properties.
Reflexive, Symmetric, and Transitive Properties
Daily Double-
-Reflexive: An angle being congruent to itself
-Symmetric: Line segment AB is congruent to Line segment CD and vice versa.
-Transitive: Line segment AB is congruent to Line segment CD and Line Segment CD is congruent to Line Segment EF, therefore, line segment AC is congruent to Line segment EF
What is the Reflexive Property of Algebra?
That something is equal to itself. Example x = x
What are the Four forms of a Conditional? 100 Points for each correct answer.
If p, then q
p implies q
p only if q
q if p
What are some reasons used in a proof? 200 points for each correct answer.
1) Given Information
2) Definitions
3) Postulates (Geometric or Algebraic)
4) Theorems that have already been proved
What is the Associative Property for Addition? Multiplication?
(a + b) + c = a + (b + c) {Addition}, (ab)c = a(bc) {Multiplication}
What is the Symmetric Property of Algebra?
If a = b, then b = a
What is a Biconditional Statement?
Daily Double: Give an example of a Biconditional statement and show how it is Biconditional.
A statement that contains if and only if (iff) signaling that both a conditional and its converse are both true.
Daily Double: Angles are congruent if and only if they have equal measures.
What differentiates a Theorem from a Postulate?
A postulate is a basic assumption, whereas Theorems must be proven using deductive reasoning and logic.
What is the Distributive Property?
a(b + c) = ab + ac
What is Transitive Property of Algebra?
If a = b and b = c, then a = c