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Warm Up March 18. Find x 2. Find x. R. 23. x. 2x-1 °. 4x °. x °. 2. 13. S. T. EOCT Week 10 #2. QUIZ on Friday March 21 st !!!. 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. C F ,. BC EF. - PowerPoint PPT Presentation
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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