4.5 Day 1 Proving ∆s CongruentSSS and SAS

Learning Target : I can compare triangles and explain if they are congruent.

(G-Co.8)

So far if want to show triangles ≅ then we need to show all 6 parts ≅, not anymore :)

Side Side Side Congruence Postulate (SSS)

A

B

C

D

E

F

If show:then:

If 3 sides of one Δ is ≅ to 3 sides of another Δ, then the 2 Δs are ≅.

Side Angle Side Congruence Postulate (SAS)

R

S

T

W

XY

If RS ≅ XW, _____ ≅ _____, and ST ≅ WY,

then _______ ≅ _______

If 2 sides and included∠ of a Δ are ≅ , then Δs are ≅

1. GIVEN: AB ≅ DE, BC ≅ EF,

_____ ≅ _____

Use the SSS Congruence Postulate.

2. GIVEN: ∠ B ≅ ∠ E, BC ≅ EF ,

_____ ≅ _____

Use the SAS Congruence Post.

State the third congruence that must be given to prove that ΔABC ≅ ΔDEF using the indicated postulate or theorem.

Decide whether enough information is given to prove that the ∆s are ≅. If yes, state which reason you would use and write a congruency statement.

A

BC

D

3. 4.

YES or NO

If YES, SSS or SAS

∆ABC ≅ _____

YES or NO

If YES, SSS or SAS

∆LMN≅ _____

5. 6.

YES or NO

If YES, SSS or SAS

∆EFG ≅ _____

YES or NO

If YES, SSS or SAS

∆EFG ≅ _____

7.D

E

F

G

Given: DE ≅ DG , EF ≅ FG

Prove: ∆DEF ≅ ∆DGF

DE ≅ DG Given

Given: MP ≅ NP, OP bisects ∠MPN

Prove: ΔMOP ≅ ΔNOP

8.

Prove: ∆ACM ≅ ∆BDM

Given: AC ≅ BD

M is midpoint of ABBA

DC

M

9.A and B are right s

A and B are right s

AC ≅ BD Given

Given

GivenM is midpoint of AB

∆ACM ≅ ∆BDM

Assignment:

4.5 Day 1

Worksheet

4.5 Day 1 Wksht Answers1. ∠C 2. ∠ABD

3. ∠D ≅ ∠M

4. EF ≅ NO

5. Yes, SSS, ∆DBE 6. Yes, SAS, ∆RQS 7. No

8. Yes, SSS, ∆PQM 9. Yes, SAS, ∆JKH 10. Yes, SAS, ∆MLN

#11- #14 MARK Pictures!!! TRY on your own!