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.

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4-4 Proving Congruence- SSS, SAS

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4 4 proving congruence sss sas

4-4 Proving Congruence- SSS, SAS


Congruent

Congruent

  • Means that corresponding parts are congruent,

  • Matching sides and angles will be congruent


4 4 proving congruence sss sas

B

A

C

Y

X

Z


Naming

Naming

  • ORDER MATTERS!!!!


Example 1

Example 1

  • If two triangles are congruent…

    • Name all congruent angles

    • Name all congruent sides

R

X

S

T

Y

Z


Reminder

Reminder…

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


Keep in mind

Keep in mind

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


Side side side congruence sss

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

Included angles


Side angle side congruence sas

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


4 4 proving congruence sss sas

Given that RQ||TS and RQ TS, Prove

RQ||TS

Given

Alt. int. <‘s are congruent

Given

Reflexive

R

S

SAS

Q

T


4 4 proving congruence sss sas

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 congruence asa and aas

4-5 Proving CongruenceASA and AAS


Angle side angle congruence asa

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.


4 4 proving congruence sss sas

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

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.


4 4 proving congruence sss sas

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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