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,