Warm Up March 18

Warm Up March 18

1. FIND X 2. FIND X

x23

132

2x-1°

x°

R

S T4x°

EOCT Week 10 #2

QUIZ on Friday March 21st!!!

A theorem is any statement that you can prove. Once you

have proven a theorem, you can use it as a reason in later

proofs.

Prove the AAS Congruence Theorem

Prove the Angle-Angle-Side Congruence Theorem.

Write a proof.

GIVEN BC EF A D, C F,

PROVE ABC DEF

Example #2 – SAS – Postulate

S

N

L

W

K

Given: N is the midpoint of LW N is the midpoint of SK

Prove: LNS WNKV V

N is the midpoint of LWN is the midpoint of SK

Given

,LN NW SN NK Definition of Midpoint

LNS WNK Vertical Angles are congruent

LNS WNKV V SAS Postulate

Example #3 – ASA – Postulate

W

HA

KS

AW WK

Given: HA || KS

Prove: HAW SKWV V

HA || KS, Given

HAW SKW Alt. Int. Angles are congruent

HWA SWK Vertical Angles are congruent

HAW SKWV V ASA Postulate

AW WK

A line to one of two || lines is to the other line.A line to one of two || lines is to the other line.

Example #5 – Column Proof

NM

Q

O

P

|| ,QM PO QM MO

QM PO

Given:

Prove: QN PN

|| ,

,

QM PO QM MO

QM PO MO

GivenGiven

PO MO

has midpoint Nhas midpoint N

90

90

om QMNom PON

Perpendicular lines intersect at 4 right Perpendicular lines intersect at 4 right angles.angles.

QMN PON Substitution, Def of Congruent AnglesSubstitution, Def of Congruent Angles

MO ON Definition of MidpointDefinition of Midpoint

QMN PONV V SASSAS

QN PN CPCTCCPCTC