definition of perpendicular lines (important): two lines that intersect to form right angles! a line...

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 __________ and ___________

If two lines are perpendicular, then they form a ___________.

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

2.2 – Definitions and Biconditional Statements

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

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.

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

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

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

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

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.

Warm – Up: Graph the following 4 equations.

y = 0 x = 0

y = x y = -x

2.4 – Reasoning with Properties from Algebra

dbcathendcandbaIf ,

dbcathendcandbaIf ,

cbcathenbaIf ,

c

b

c

athencandbaIf ,0

)(

,

inequalityorequationanyin

otherthefordsubstitutebemay

boraeitherthenbaIf

aa

abthenbaIf ,

cathencbandbaIf ,

Reasons

13125 x

Reasons

522

1x

Reflexive Prop. Of equality

Symmetric Prop. Of equality

Transitive Prop. Of equality

DmDmDEDE

DmEmthenEmDmIf

DEFGthenFGDEIf

,

,

FmDmthen

FmEmandEmDmIf

JKDEthen

JKFGandFGDEIf

,

,

We will fill in the blanks

M A T H AHMT:Prove

THMA:Given

THMA 1)

2)

3)

4)

5)

1)

2)

3)

4)

5)

Prop Reflexive

THATATMA

Post AddSegment

AHMT

D

U C

K12

021m:Prove

50UDKm,302m:Given

50UDKm

,302m1)

2)

3)

4)

5)

1)

2)

3)

4)

5)

Post Add Angle

PropSubst

3030

021m

A N G

SE LSAGroveP

LENGESANGiven

:

,:

L

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.

2.6 – Proving Statements about Angles

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 _____ and _____ are supplementary and _____ and ____ are supplementarythen ________

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

If _____ and _____ are complementary and _____ and ____ are complementarythen ________

Explain in your own words why congruent supplements theorem has to be true. This may show up on your test.

Vertical Angles Thrm - _____ angles are ______

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

IASm

RALm

RAIm

WAIm

Find

35IAOm

ary.complement are OAZ and IAO

W

RI

O

ZS

A

L

4m

3m

2m

Find

551m

.3 2

ary.supplement are 4 and 3

ary.supplement are 2 and 1

E

R A

T1 2

90ERAmGiven

Provearycomplement

areand 21

12

3pairlinare

pairlinare

.3,2

.2,1

Given

Prove 31 mm

pairlinare

pairlinare

.3,2

.2,1

anglespare

anglespare

sup3,2

sup2,1

Def of Supp Angles

P

K M

N5 6

JKNmmm 65

PKMmJKNm

Given

Prove

75 mm

J 7

2.5-9 Number 2

V

Q

R

T

89

PQTmmm 98

Substitution Prop =

VQRmPQTm Given

Prove 108 mm

P 10