Date post: | 01-Apr-2015 |
Category: |
Documents |
Upload: | william-glass |
View: | 220 times |
Download: | 3 times |
Chapter 2
By: Nick Holliday Josh Vincz, James Collins, andGreg “Darth” Rader
Section 1 Vocab● Conditional statement- statement with a
hypothesis and a conclusion● Hypothesis- “if ” part of a conditional statement. ● Conclusion- “then” part of the conditional
statement● If then form- if contains the hypothesis and then
contains the conclusion● Converse- The statement formed by switching the
conclusion and the hypothesis● Negation- The negative of a statement● Inverse- The statement formed when you negate
the hypothesis and conclusion of the converse.
Section 1 Vocab Continued
● Contrapositive- The statement formed when you negate the hypothesis and conclusion of a conditional statement.
● Equivalent statement- 2 statements that are both true or that are both false.
Example 1
● Rewrite the conditional statement. ● An even number is divisible by 2● Conditional statement = If it is an even number
Then it is divisible by 2
Example 2
● Write the (a inverse, (b converse, (c contrapositive of the following statement.
● If it is Friday then there is no school tomorrow.● (a Inverse: If it is not Friday, then there is school
tomorrow.● (b Converse: If there is no school tomorrow, then
it is Friday.● (c Contrapositive: If there is school tomorrow,
then it is not Friday.
Checkpoint
● Write the inverse, converse, and contrapositive of the conditional statement.
● If Josh is complaining about a test score Then he was in Mrs. Wagner's class.
●
Point line and plane postulate`
● Post 5: Through any two points there exists exactly one line
● Post 6: A line contains at least two points● Post 7: If two lines intersect then their intersection is one
point● Post 8: Through any three non colinear points there exists
one plane● Post 9: A plane contains at least three noncolinear points● Post 10: If two points lie in a plane, then the line
containing them lies in the plane● Post 11: If two planes intersect, then their intersection is a
line
Section 2 vocab
● Perpendicular lines – two lines that form a right angle.
● Line perpendicular to a plane- intersects plane at point that is perpendicular to every line.
● Bioconditional statement- a statement that contains if and only if and conditional and converse.
Example
● If it is an equailateral triangle then all angles on the triangle are congruent.
● If all the angleson the triangle are congruent then it is an equalaterial triangle
● Since both statements are true the biconditional statement is...
● It is an equalateral triangle if and only if all of the angles on the triangle are congruent.
Section 3 Vocab
● Logical argument- an argument based on deductive reasoning which uses facts, definintions, and accepted properties in a logical order
● Law of Detachment- If pq is a true conditional and p is true then q is true
● Law of Syllogism- If p and qr are true conditional statements, then pr is true
Other notes of section 3
● P hypothesis● Q conclusion● Conditional statement = pq● Converse = qp● Biconditional statement = p<q or ● P if and only if Q● ~ negate that portion of the statement
Example
● Let p be value of x is 7. Let q be x is <10. ● Write p—q in words then write q—p in words.● Decide whether the Biconditional statement p<>q
is true.
Algebraic properties of equality
● Let a b and c be real numbers. ● Addition property- if a= b then a+c=b+c● Subtraction property- if a=b then a-c=a-b
Multiplication property- if a=b then ac=bc● Division property- if a=b and c does not = c then
a/c=b/c● Reflexive property- for any real number a, a=a● Symmetric property- if a=b then b=a● Transitive property- if a=b and b=c then a=c● Substitution property- if a=b, then a can be
substituted for b in any equation
Properties of Equality
● Segment Length● Reflexive- For any segment AB AB=AB● Symmetric- If AB=CD then CD=AB● Transitive- If AB=CD and CD=EF then AB=EF● Angle Measure● Reflexive- For any angle A m<A =m<A● Symmetric- If m<A=m<B then m<B=m<A● Transitive- If m<A=m<B and m<B=m<C, then
m<A=m<C
Example
● Solve the following equations -2x +1 =56 -3x 5x + 12 = 2 + 10x
Section 5 vocab
Theorem- A true statement that follows as a result of other true statements
Two-column Proof- A type of proof written as numbered statement and reasons that show a logical argument
Paragraph Proof- type of proof written as a paragraph.
Theorem 2.1
● Reflexive- for any segment ab, ab is congruent to ab.
● Symmetric- if ab is congruent to cd then cd is congruent to ab.
● Transitive- if ab is congruent to cd and cd is congruent to ef then ab is congruent to ef.
Example
● Given JK is congruent to MN. MN is congruent to PQ. Prove JK is congruent to PQ
Section 2.6
● Theorem 2.2 properties of angle congruences.● Reflexive- for any angle a, a=a● Symmetric- if angle a is congruent to angle b then
angle b is congruent of angle a.● Transitive- if angle a is congruent to angle b and
angle b is congruent to angle c then angle a is congruent angle c.
Example
● Given that angle 4 is congruent to angle 6 and angle 6 is congruent to angle 8. The measure of angle 8 is 77. what is the measure of angle 4. explain your reasoning.
Theorem 2.3+ theorem 2.4
● All right angles are congruent. ● If two angles are supplementary then they are
congruent. ● If angle 1 + angle 2 = 180 and angle 2+ angle 3 =
180 then angle 1 and angle 3 are congruent.
Theorem 2.5
● If two angles are complementary to the same angle then the two angles are congruent
● If angle 4 + angle 5=90 and angle 5+angle 6=90 then angle 4 = angle 6
Example
● Given angle 1 and angle 2 are complements, angle 3 and angle 4 are complements, angle 2 and angle 4 are congruent. Prove angle 1 and angle 3 are congruent,