Proving Triangles Congruent

SSS Postulate, SAS Postulate

ASA Postulate, AAS Theorem

& HL Theorem

Side - Side - Side Postulate

• If three sides of one triangle are congruent to three sides of another triangle, then

• the two triangles are congruent.

• ABC DEF

A C

B

F

E

D

SSS Example:

E

T

I

K

ITK

ETK

Side - Angle - Side Postulate

• If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then

• the two triangles are • JKL MNO

O

N

M

J L

K

SAS Example

ARK ?

ERN

K N

E

R

A

Angle - Side - Angle Postulate

• If two angles and the included side of one triangle are to two angles and the included side of another triangle, then

• the triangles are • PQR STU

U

T

S

R Q

P

ASA Example

MY

R

A

AY Bisects < MAR

YMA ?

YRA

Angle - Angle - Side Theorem• If two angles and a

nonincluded side of one triangle are to two angles and the corresponding nonincluded side, then

• the triangles are • XYZ JAC

C

J A

Z

Y X

AAS Example

K Y

RE

RKY ? KRE

Hypotenuse-Leg Theorem• If the hypotenuse

and a leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then

• the triangles are • RPW SBM

R

P W

S

B M

QMC ?

QHC

Q

HC

M

HL Example

Example 1

ME

K

I

IEM ? IEK

Property?

SAS

Example 2

RBA ? IBT

Property?

ASA

R

T

IB

A

Example 3

MOU ?None

Property?None: SSA

isn’t a property

M

E

SU

O

Example 4

RIK ? SKI

Property?

SSS

K

S

I

R

Example 5

SIL ?

LAS

Property?

AAS

L A

SI

RBI ? GBI

Property?

HLI

R GB

Example 6

MISSING PARTS

What information do you need to prove the following triangles are congruent by SAS?

Q

W

E

RT

RWQW

MISSING PARTS

What information do you need to prove the following triangles are congruent by ASA?

FDGADS

A S

D F

G

63o

63o

MISSING PARTS

What information do you need to prove the following triangles are congruent by AAS?

YUIITY

T Y

UI

MISSING PARTS

What information do you need to prove the following triangles are congruent by SSS?

VCYB

Y

C

V

B

6

6

MISSING PARTS

What information do you need to prove the following triangles are congruent by HL?

HQMQ

HCMC

OR

Q

HC

M