Upcoming SlideShare
×

# Chapter 2 Review

611 views

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
611
On SlideShare
0
From Embeds
0
Number of Embeds
21
Actions
Shares
0
5
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Chapter 2 Review

1. 1. <ul><li>Terms To Know  </li></ul><ul><li>  Ad jacent angles - angles in a plane that have their vertex have one side in common but no interior points on common. </li></ul><ul><li>B iconditional - &quot;if and only if&quot; statement: If and only if the shape is a equilateral quadrilateral with 4 right angles, then the shape is a square. </li></ul><ul><li>C onditional - &quot;if - then&quot; statements, the &quot;If&quot; part is the Hypothesis part is the Conclusion : If a shape is a square, then the shape is a rectangle. </li></ul><ul><li>C onverse - to create a converse from a conditional, switch the hypothesis and conclusion. </li></ul><ul><li>C ounterexample - an example that disproves a conditional. </li></ul><ul><li>D eduction - the process of drawing logical conclusions by an argument. </li></ul><ul><li>E quivalence R elation - any relation that satisfies the reflexive property, symmetric property and the transitive property. </li></ul>
2. 2. <ul><li>2.1 </li></ul><ul><li>Proofs: </li></ul><ul><li>Two Column Proofs: on the left side, is a statement, on the right side is the justification for the statement. </li></ul><ul><li>use postulates and theorems to help justify your statements in proofs </li></ul>
3. 3. <ul><li>2.2 </li></ul><ul><li>Conditionals: </li></ul><ul><li>Euler diagrams: like venn diagrams, its an easy way to see statements. </li></ul><ul><li>If p then q. </li></ul><ul><li>Logical Chains: </li></ul><ul><li>can be drawn from deductive reason. </li></ul><ul><li>three parts. </li></ul><ul><li>2.2.1 </li></ul><ul><li>“ If-Then ” Transitive property </li></ul><ul><li>Given: &quot;If A then B, and if B then C.&quot; </li></ul><ul><li>You can conclude: &quot;If A Then C&quot; </li></ul><ul><li>E.g.: If a tiger is a cat, and a cat is an animal, then a tiger is an animal. </li></ul><ul><li>E.g.: If an animal is a cow, then it is fat. </li></ul><ul><li>Larry is a cow. </li></ul><ul><li>Conclusion: Larry is fat </li></ul><ul><li>Converse: If an animal is fat, then it is a cow </li></ul>
4. 4. <ul><li>2.3 </li></ul><ul><li>Adjacent Angles: </li></ul><ul><li>are next to each other (in simple terms). </li></ul><ul><li>the vertex is the same. </li></ul>
5. 5. <ul><li>2.4.1 </li></ul><ul><li>Addition Property </li></ul><ul><li>If a = b, then a + c = b + c </li></ul><ul><li>Explanation: </li></ul><ul><li>a = b </li></ul><ul><li>a + c = b + c </li></ul><ul><li>Substitute b for a, or substitute a for b. </li></ul><ul><li>a + c = (a) + c OR (b) + c = b + c </li></ul><ul><li>a + c = a + c OR b + c = b + c </li></ul><ul><li>2.4.2 </li></ul><ul><li>Subtraction Property </li></ul><ul><li>If a = b then a – c = b – c </li></ul><ul><li>Explanation: </li></ul><ul><li>a = b </li></ul><ul><li>a – c = b – c </li></ul><ul><li>Substitute b for a, or substitute a for b. </li></ul><ul><li>a – c = (a) – c OR (b) – c = b – c </li></ul><ul><li>a – c = a – c OR b – c = b – c </li></ul>
6. 6. <ul><li>2.4.3 </li></ul><ul><li>Multiplication Property </li></ul><ul><li>If a = b then a c = b c </li></ul><ul><li>Explanation: </li></ul><ul><li>a = b </li></ul><ul><li>a c = b c </li></ul><ul><li>Substitute b for a, or substitute a for b. </li></ul><ul><li>a c = (a) c OR (b) c = b c </li></ul><ul><li>a c = a c OR b c = b c </li></ul><ul><li>2.4.4 </li></ul><ul><li>Division Property </li></ul><ul><li>If a = b and c is not equal to 0 then a / c =b / c </li></ul><ul><li>Explanation: </li></ul><ul><li>a = b </li></ul><ul><li>a / c = b / c </li></ul><ul><li>Substitute b for a, or substitute a for b. </li></ul><ul><li>a / c = (a) / c OR (b) / c = b / c </li></ul><ul><li>a / c = a / c OR b / c = b / c </li></ul>
7. 7. <ul><li>2.4.5 </li></ul><ul><li>Substitution Property </li></ul><ul><li>If a=b, you may replace a with b in any true equation containing a and the resulting equation will still be true </li></ul><ul><li>Example: </li></ul><ul><li>a=5 </li></ul><ul><li>2a^2 - 35 = 2a^2 - 6a - 5 </li></ul><ul><li>Substitute a for 5 </li></ul><ul><li>2(5)^2 - 35 = 2(5)^2 - 6(5) - 5 </li></ul><ul><li>2(25) - 35 = 2(25) - 30 - 5 </li></ul><ul><li>50 - 35 = 50 - 30 - 5 </li></ul><ul><li>15 = 15 </li></ul><ul><li>2.4.6 </li></ul><ul><li>Overlapping Segments Theorum </li></ul><ul><li>Given a segment with points A, B, C, and D the following statements are true: </li></ul><ul><ul><li>1. If AB=CD, then AC=BD </li></ul></ul><ul><ul><li>2. If AC=BD, then AB=CD </li></ul></ul>
8. 8. <ul><li>2.4.7 </li></ul><ul><li>Reflexive Property of Equality </li></ul><ul><li>For any real number a, a=a </li></ul><ul><li>E.g.: 1 = 1 </li></ul><ul><li>2.4.8 </li></ul><ul><li>Symmetric Property of Equality </li></ul><ul><li>For all real numbers a and b, if a=b, then b=a </li></ul><ul><li>E.g.: 1 = 1 ² , then 1 ² = 1 </li></ul>
9. 9. <ul><li>2.4.9 </li></ul><ul><li>Transitive Property of Equality </li></ul><ul><li>For all real numbers a, b, and if a=b and b=c, then a=c </li></ul><ul><li>E.g.: 1 = 1 ², 1² = 1³, then 1 = 1³ </li></ul><ul><li>2.4.10 </li></ul><ul><li>Reflexive Property of Congruence </li></ul><ul><li>figure A is congruent to figure a </li></ul>
10. 10. <ul><li>2.4.11 </li></ul><ul><li>Symmetric Property of Congruence </li></ul><ul><li>If figure A is congruent to figure B, then figure B is congruent to figure A </li></ul><ul><li>2.4.12 </li></ul>