Triangle Congruence Theorems and Proofs

Which postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent?

• SAS

• SSS

• ASA

• AAS

If two triangles have two angles and the included side congruent, which postulate can be used to prove their congruence?

• SSS

• ASA

• SAS

• AAS

In the example with triangles ABC and DEF, if AB is congruent to DE, BC is congruent to EF, and AC is congruent to DF, which postulate is used to prove their congruence?

• SAS

• ASA

• AAS

• SSS

For triangles RST and VXY, if angle S is congruent to angle X, RS is congruent to VX, and angle R is congruent to angle V, which postulate is used?

• SAS

• ASA

• AAS

• SSS

When dealing with composite triangles, what is a useful strategy to prove congruence?

• Use only the SSS postulate

• Ignore the common side

• Split the composite triangle into two smaller triangles

• Use the AAA postulate

In a composite triangle, if AD is congruent to CD and AB is congruent to BC, what can be concluded about triangles ABD and CBD?

• They are congruent by the AAS postulate

• They are congruent by the SSS postulate

• They are congruent by the ASA postulate

• They are not congruent

What is the first step in writing a two-column proof?

• State the given information

• Write the conclusion

• Identify the postulate to be used

• Draw the triangles

In a two-column proof, if segment AB is congruent to segment CD and segment AE is congruent to segment DE, which postulate can be used to prove triangle ABE is congruent to triangle CDE?

• AAS

• SAS

• ASA

• SSS

If points B and C trisect segment AD, what can be concluded about segments AB, BC, and CD?

• BC is not congruent to AB

• AB is half the length of CD

• AB, BC, and CD are congruent

• AB is twice the length of CD

In the final example, if angle A is congruent to angle D and angle EBC is congruent to angle ECB, what can be concluded about triangles EAB and EDC?

• They are congruent by the ASA postulate

• They are not congruent

• They are congruent by the AAS postulate

• They are congruent by the SSS postulate