Reasoning
Conjecture is and educated guess.
Inductive Reasoning is looking at several specific situations to arrive at a conjecture.
If-Then Statements are called conditional statemtents.
If
part is the hypothesis.
Then part is the conclusion.
Statement: All angles are measured in degrees.
If-then form: If an object is an angle then it is measured in
degrees.
Other forms of if-then statements:
Statement: If p then q.
Ex: If an object is a triangle then it has 3 sides.
* ~
means not
| Converse | If q then p | If an object has 3 sides then it is a triangle. |
| Inverse | If ~p then ~q | If an object is not a triangle then it doesn't have 3 sides. |
| Contrapositive | If ~q then ~p | If an object doesn't have 3 sides then it is not a triangle. |
*
The statement and the contrapositve are logically equivalent.
(If the statement
is true then the contrapositive is also try but the converse and inverse may
be false.)
Properties of Equality
| Reflexive Property | a = a |
| Symmetric Property | If a = b then b = a |
| Transitive Property | If
a = b, b = c, then a = c (take out middle) |
| Addition Property | If 3x-4 = 8 then 3x = 12 |
| Subtraction Property | If 2x+7=9 then 2x = 2 |
| Multiplication Property | If 1/4x = 8 then x = 32 |
| Division Property | If 5x = 20 then x = 4 |
| Substitution Property | If a = x and b = x then a = b |
| Distributive Property | If a(x+y) then ax+ay |
Example Problems
1. Write in if-then form: Acute angles are less than 90 degrees.
2. Write the converse, inverse, and contrapostive:
If
Ð1
= 95 degrees then it is an obtuse angle.
Name the properties:
3. x = y then y = x
4. 8x+3 = 19 then 8x = 16
5. If a + b = 15 and a = 8 then 8 + b = 15
6. If lm = no and no = pq then lm = pq.
7. If 9x = 54 then x = 6
8. If GF = GF
9. If 7x - 4 = 17 then 7x = 21
10. If 3(x+2) = 3x + 6
 |
 |