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CONGRUENT TRIANGLES

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CONGRUENT

TRIANGLES

Sections 4-4

SSS

If three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent.

Methods of Proving Triangles Congruent

SAS

If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

ASA

If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

AAS

If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

HL

If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are congruent.

Congruent Triangles

Name the congruence

Is

?

FRS

PQD

R

P

120°

Q

F

120°

35°

D

35°

ASA

S

Congruent Triangles

Name the congruence

Is

QSR ?

FRS

R

Q

42°

42°

F

Shared Side – Reflexive Prop

S

WHY NOT?

SSA

SSA is NOT a valid Triangle congruence

Congruent Triangles

Name the congruence

Is

?

FRS

QSR

R

50°

Q

F

Shared Side – Reflexive Prop

50°

S

SAS

Congruent Triangles

Name the congruence

Is

?

MNR

PTB

B

R

N

P

SSS ?

T

M

WHY NOT?

Names of the triangles in the congruence statement are not in corresponding order.

A

C

Writing a PROOF

B

Given: AB = BD

EB = BC

Prove: ∆ABE ˜ ∆DBC

1

2

=

SAS

E

D

A

C

Given: AB = BD

EB = BC

Prove: ∆ABE ≅ ∆DBC

B

1

2

SAS

E

D

STATEMENTS REASONS

AB ≅ BD Given

<1 ≅ <2 VA

EB ≅ BC Given

∆ABE ≅ ∆DBC SAS

C

Given: CX bisects ACB

A ≅ B

Prove: ∆ACX≅∆BCX

2

1

AAS

B

A

X

CX bisects ACB Given

1 ≅ 2 Def of angle bisector

A ≅ B Given

CX ≅ CX Reflexive Prop

∆ACX ∆BCX AAS

≅

Can you prove these triangles

are congruent?

A

Given: AB llDC;

X is the midpoint of AC

Prove: AXB ˜ CXD

B

X

=

D

C

A

B

X

Given: AB ll DC

X is the midpoint of AC

Prove: AXB ˜ CXD

D

C

=

ASA