Flowchart Proof on Triangle Congruence

(with CPCTC)

1. Given: Prove:

NA ST,SA NT NAT STA

2. Given: Prove:

A S

TN

S

V Z

OL

E

LO ZV,SL || EZ

OS VE

O V

SA NTNA ST AT AT

NAT STA

ANT TSA

Given Given Reflexive

SSS Triangle Congruence conj.

CPCTC

LO ZV

SL || EZ

21

1 2 O VGiven AIA // Lines conj. Given

LSO ZEVSAA Triangle cong. conj.

OS VECPCTC

Reflection: Extending our proof, what can we conclude from NATSTA? NA //ST by the Converse of AIA // Lines

ConjGiven

3. Given: Prove:

4. Given: Prove:

OS OV E L

L E

V S

O

LO EO

1 2

1 2OS OV LO EOGiven

SAS Triangle cong. conj.

Vertical Angles conj

Given

LOV EOS

E LCPCTC

S

N

D

Y

A

R

SR SA, SN SY

N Y SN SYSR SA S S

NSR YSA

N Y

Given GivenReflexive Property

SAS Triangle cong. conj.

CPCTC

5. Given:

Prove:

Given

Given

CPCTC

RIA is isosceles with vertex RIA RIT AIT

T

I

R A

RIA is isosceles with vertex RIA

RIT AIT

RT AT

RT AT

AIRI

IT IT

AR

ASA Triangle Cong. Conj.

ITC Def. of iso triangle

AITRIT

If there is no line coming from the topmost box, the 1st box on the left may be replaced by and the triangles will be by SAS Triangle Conj.

6. Given: Prove:

JS JG, JSN JGOJNO is isosceles

J

ON

G S

JGJS JGOJSN JJ

ASATriangle Cong. Conj.

Given

Given

Reflexive Prop.

JGOJSN

JOJN

JNO is isoscelesDef. of iso triangle

CPCTC