SSS and SAS Congruence

4-4 HG SSS, SAS

Triangle Rigidity

Triangle Congruence "Shortcuts" Postulates

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SSS

• SAS

• Not congruent

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SSS

• SAS

• Not congruent

Multiple Choice

Which triangle congruence theorem proves the two triangles congruent?

• SAS

• SSS

• not enough information

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SAS

• SSS

• Not congruent

Multiple Choice

What additional information is required for the two triangles to be congruent by SSS?

• A
• B
• C
• D

Multiple Choice

What additional information is required to prove the two triangles are congruent by SSS?

• A)

• B)

• C)

• D)

Multiple Choice

What additional information is required to prove the two triangles are congruent by SAS?

• A)

• B)

• C)

• D)

Multiple Choice

Which congruency statement can be written for the triangles pictured?

• ΔABC ≅ ΔEDC

• ΔACB ≅ ΔEDC

• ΔECD ≅ ΔCAB

SSS Proofs

Example 1

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• AAS

• SSS

• Not enough information given

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SAS

• Not enough information

• SSS

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• Not congruent

• SSS

• SAS

Multiple Choice

Which triangle congruence theorem can be used to prove the triangles are congruent?

• SSS

• Not congruent

• SAS

Multiple Choice

What are the 2 missing pieces of information?

• Transitive Property, SAS(Side-Angle-Side)
• Reflexive Property, SAS(Side-Angle-Side)
• Transitive Property, SSS(Side-Side-Side)
• Reflexive Property, SSS(Side-Side-Side)

SSS Proofs

Example 2

Multiple Choice

Identify the  missing statement or reason

• Definition of Angle Bisector
• Alternate Interior Angles Theorem
• Reflexive Property
• Definition of Midpoint

Multiple Choice

What is reason #3?

• SAS

• Vertical Angle Theorem

• SSS

• Definition of Congruent Triangles

SAS Proofs

Example 4

Multiple Choice

What is reason #2?

• Vertical angles are congruent.

• Consecutive angles are congruent.

• Alternate interior angles are congruent.

• Definition of Bisector

Multiple Choice

What is reason #4?

• Reflexive Property

• Definition of Midpoint

• Vertical angles are congruent.

• Given

Multiple Choice

What is statement #6?

• $$\overline{BC}\ \cong\ \overline{BC}$$
  

• $$\overline{BC}\ ≅\ \overline{DA}$$
  

• $$∠BCD\ ≅\ \angle BAC$$

• $$\overline{AB}\ ≅\ \overline{CD}$$

SAS Proof

Example 5

Multiple Choice

What is statement #4?

• ∆HFG≅∆IHF

• ∆FHG≅∆IHF

• ∆GFH≅∆IFH

• ∆HFG≅∆IFH

Multiple Choice

Fill in the missing proofs.

• Transitive Property, SAS(Side-Angle-Side)
• Reflexive Property, SAS(Side-Angle-Side)
• Reflexive Property, Vertical Angles Thm.
• Transitive Property, SSS(Side-Side-Side)

SAS Proof

Example 7

Multiple Choice

Why is ∠KMJ ≌∠LJM?

• Alternate Exterior angles are congruent

• Alternate Interior Angles are congruent

• Corresponding Angles are Congruent

• Consecutive Interior angles are supplementary

Multiple Choice

17. Choose the correct reason for line 3.

• Given

• Def of Midpoint

• Def of Bisector

• Reflexive Property

Multiple Choice

18. Choose the correct reason for line 5.

• SSS

• SAS

• Given

• Definition of Midpoint