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4-4 Proving Congruence- SSS, SAS. Congruent. Means that corresponding parts are congruent, Matching sides and angles will be congruent. B. A. C. Y. X. Z. Naming. ORDER MATTERS!!!!. Example 1. If two triangles are congruent… Name all congruent angles Name all congruent sides. R.

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4-4 Proving Congruence- SSS, SAS

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4-4 Proving Congruence- SSS, SAS


Congruent

  • Means that corresponding parts are congruent,

  • Matching sides and angles will be congruent


B

A

C

Y

X

Z


Naming

  • ORDER MATTERS!!!!


Example 1

  • If two triangles are congruent…

    • Name all congruent angles

    • Name all congruent sides

R

X

S

T

Y

Z


Reminder…

  • If two angles of one triangle are congruent to two angles of another triangle then the 3rd angles are congruent


Keep in mind

  • You can flip, turn or slide congruent triangles and they will maintain congruency!!


Side-Side-Side Congruence (SSS)

  • If the sides of one triangle are congruent to the sides of a second triangle, then the triangles are congruent

X

Y

B

A

Z

C


Included angles


Side-Angle-Side Congruence (SAS)

  • If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle, then the triangles are congruent.

B

D

E

F

C

A


Given that RQ||TS and RQ TS, Prove

RQ||TS

Given

Alt. int. <‘s are congruent

Given

Reflexive

R

S

SAS

Q

T


Given: Triangle CDE is an isosceles triangle. G is the midpoint of CE.

Prove:

D

E

C

G

Statement

Reason

  • Given

  • Def. of Isosceles Triangle

  • Midpoint theorem

  • Reflexive property

  • SSS

1

Triangle CDE is isosceles

2

CD = ED

3

CG = GE

4

DG = DG

5


4-5 Proving CongruenceASA and AAS


Angle-Side-Angle Congruence(ASA)

  • If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle, then the triangles are congruent.


Given: L is the midpoint of WE and WR||ED

Prove:

E

R

L

D

W

<W <E because_________________ angles are ____________. By the___________________,

WL___EL. Since vertical angles are _____________,

______________ and by ______

Alternate interior

Congruent

Def. of midpoint thrm

Congruent

=

<RLW = <ELD

ASA


Angle-Angle-Side Congruence(AAS)

  • If 2 angles and a non-included side of one triangle are congruent to the corresponding 2 angles and side of another triangle, then the 2 triangles are congruent.


Given: <NKL <NJM and

Prove:

K

J

M

L

N

Statement

Reason

Given

1. <NKL <NJM

1. ____________

2. <N <N

Reflexive

2.____________

KL = MN

3._____________

3. Given

4. AAS

4.

5. CPCTC

5.___________


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