2.1 Conditional StatementsNote, there will be a notes

handout for 2.1 given in class.

A Conditional Statement has TWO parts, the HYPOTHESIS and

CONCLUSION

In if-then form

If -> HYPOTHESIS p

Then -> CONCLUSION q

(it’s not necessarily these letters all the time)

Writing a statement in if-then form.People who go to USC need help.If you go to USC, then you need help

A Troy student is a Warrior.If you are a Troy student, then you are a Warrior.

All mountains have rocks.If it is a mountain, then it has rocks.

A lover of potatoes is a lover of French fries.If you love potatoes, then you love French fries.

Write the statement in if-them form.

It just takes one COUNTEREXAMPLE to prove something is wrong.

If x2 = 25, then x = 5False, x = -5

If you go to USC, then you are smart.False, virtually every USC student

All triangles are equilateralFalse, some triangles have different side lengths.

All even numbers can be divided by 2.True

A CONVERSE is when you reverse the original conditional statement.

If you are in room 302, then the room is cold.

If it is cold, then you are in room 302.

The converse is NOT always true!!!!

Write the converse and say whether it is true, or state a counterexample.

If a student is in room 302, the student is in math class.

If a student is in math class, the student is in room 302.

Mr. Booze’s class.

A statement can be changed by negation, which is writing the negative of a statement.

If you are in room 302, you are in Mr. Kim’s class.

If you are in Mr. Kim’s class, then you are in room 302.

If you are not in room 302, you are not in Mr. Kim’s class.

If you are not in Mr. Kim’s class, you are not in room 302.

qp

pq

qp ~~

pq ~~

Conditional

Converse

Inverse

ContrapositiveNegation symbol

• Conditional If you go to Troy, then you are a student.

• Converse If you are a student, then you go to Troy.

• Inverse If you don’t go to Troy, then you’re not a student.

• Contrapositive If you are not a student, then you don’t go to Troy.

THE Conditional statement and the contrapositive are EQUIVALENT (if one is true the other is true, if one is false,

the other is false.

THE CONVERSE and INVERSE are EQUIVALENT (if one is true the other is

true, if one is false, the other is false.

Postulate 6: A line contains at least two points.

Postulate 5: Through any two points there is EXACTLY one line

Postulate 7: If two lines intersect, then they intersect in exactly one point.

Postulate 8: Through any three noncollinear points there is EXACTLY one plane.

Postulate 9: A plane contains at least three noncollinear points.

Postulate 10: If two points are in a plane, then the line that contains the points is in that plane.

If not, it’d be like this.

Postulate 11: If two planes intersect, then their intersection is a line.

P I

Z A

H U

T

Name two lines on plane AZHU that are not drawn.

ZUandAH

?IPZAplaneonisIZ

lineknowyoudoHow

If two points are on a plane, the line containing them is on the plane. (Post)

______________todue

________exactly isthere

T, U,A,pointsThrough

One plane

Postulate 8

2.2 – Definitions and Biconditional Statements

Definition of Perpendicular lines (IMPORTANT): Two

lines that intersect to form RIGHT ANGLES!

A line perpendicular to a plane is a line that intersects

the plane in a point that is perpendicular to every line in

the plane that intersects it.symbollarperpendicuAll definitions work forwards and backwards

If two lines are perpendicular, then they form a right angle.

If two lines intersect to form right angles, then they are perpendicular.

All definitions work forwards and backwards

If two lines are perpendicular, then they form a right angle.

If two lines intersect to form right angles, then they are perpendicular.

If a conditional statement and its converse are both true, it is called biconditional, and you can combine them into a “if and

only if” statement

Two intersecting lines are perpendicular if and only if they form right angles.

True or false? Why? (Check some hw)Z Y

X

W V U

TS

R

WVZ and RVS form a linear pair.

YVU and TVR are supplementary

Y, V, and S are collinear

WVT and YVX are complementary.

Write the conditional statement and the converse as a biconditional and see if

it’s true.If two segments are congruent, then their

lengths are the same.

Two segments are congruent if and only if their lengths are the same.

If the lengths of the segments are the same, then they are congruent.

TRUE!

Write the conditional statement and the converse as a biconditional and see if

it’s true.

If B is between A and C, then AB + BC = AC

B is between A and C if and only if AB + BC = AC

If AB + BC = AC, then B is between A and C

TRUE!

Write the converse of the statement, then write the biconditional statement. Then see if the biconditional statement is true or false. (Check more hw)

If x = 3, then x2 = 9

If x2 = 9, then x = 3x = 3 if and only if x2 = 9

False, x = -3 is a counterexample

If two angles are a linear pair, then they are supplementary angles.

If two angles are supplementary, then they form a linear pair

Two angles are a linear pair if and only if they are supplementary.

False, they don’t have to be on the same line.

Split up the biconditional into a conditional statement and its converse.

Pizza is healthy if and only if it has bacon.

Students are good citizens if and only if they follow the ESLRs.

2.4 – Reasoning with Properties from Algebra

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2.6 – Proving Statements about Angles

Center of compass

GREEN DOT

Writing end

DRAWN PART (compass and ruler)

Copy a segment

1) Draw a line

2) Choose point on line

3) Set compass to original radius, transfer it to new line, draw an arc, label the intersection.

Use same radius for both circles, so segments are congruent.

AA

ABAB

__________, thenBAIf

___________, thenCDABIf

___________, thenCBandBAIf

___________, thenEFCDandCDABIf

__________ Property

Symmetric Property

_________ Property

Right Angle Congruence Thrm - All ______ angles are _______

Congruent Supplements TheoremIf two angles are ____________ to the same angle (or to congruent angles), then they are congruent.

If _____ + _____ = 180 and _____ + ____ = 180, then ____ ____

Congruent Complements Theorem

If two angles are ____________ to the same angle (or to congruent angles), then they are congruent.

If _____ + _____ = 90 and _____ + ____ = 90, then ____ ____

Vertical Angles Thrm - _____ angles are ______

Linear Pair Postulate – If two angles form a linear pair, then they are _________

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