6.3 Congruent Triangles: SSS and SAS

Warm-up (IN)

Learning Objective: to prove that triangles are congruent without proving that all 6 corresponding parts are congruent.

K1. If , which angle is congruent to ?ADF BKI D

2. If , which side is congruent to ?ADF BKI KI

3. If , which side is congruent to ?ADF BKI IB

4. Name the triangles that appear to be congruent in the figure.

FA

2

V

1U

R

S T, SUR TUV RST VTS

5. How do you know

that 1 2? Vertical s

DF

Notes

Learning Objective: to prove that triangles are congruent without proving that all 6 corresponding parts are congruent

Side-Side-Side (SSS) Postulate -

A

B

C

If , and ,AB DE AC DF CB FE then ABC DEF

If 3 sides of a triangle are congruent to 3 sides of another triangle, then the triangles are congruent

D

E

F

Learning Objective: to prove that triangles are congruent without proving that all 6 corresponding parts are congruent

Given: Quadrilateral is a parallelogramABCDEX 1 –

Prove: ABC CDA

D

C

A

BStatements Reasons

1. is a parallelogramABCD 1. Given2. BC ADDC AB

2. Opp sides of a

are 3. AC AC 3. Reflexive Property4. ABC CDA 4. SSS

Learning Objective: to prove that triangles are congruent without proving that all 6 corresponding parts are congruent

Side-Angle-Side (SAS) Postulate -

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

A

B

C

D

E

F

If , and ,AB DE AC DF A D then ABC DEF

Learning Objective: to prove that triangles are congruent without proving that all 6 corresponding parts are congruent

Given:

bisects

NO NQ

NP ONQ

EX 2 –

Prove: NOP NQP Q

PN

O

Statements Reasons

1. Given

2. Def. of a bisector

3. NP NP 3. Reflexive Property

4. NOP NQP 4. SAS

1.

bisects

NO NQ

NP ONQ

QNPONP .2

Learning Objective: to prove that triangles are congruent without proving that all 6 corresponding parts are congruent

CKC p. 295– in your notes!!!

HW – p. 295 # 1-11, 20, 22

Out – Describe the SSS and SAS postulates. How do they help you prove 2 triangles are congruent?

Summary – Today, I learned…

POW!!