Day 56 Geometry

Decide whether enough information is given to prove that the triangles are congruent. If so, state the theorem you would use.

△ABC, △QRS

• yes; ASA Congruence Theorem

• yes; AAS Congruence Theorem

• yes; SSA Congruence Theorem

• No

Answer explanation

AC is congruent to US and those sides are not included between the two angles, so this example follows AAS.

Decide whether enough information is given to prove that the triangles are congruent. If so, state the theorem you would use.

△ABC, △QRS

• yes; ASA Congruence Theorem

• yes; AAS Congruence Theorem

• yes; SAS Congruence Theorem

• No

Answer explanation

BC is congruent to itself and it is not an included side, so this example follows AAS.

Decide whether enough information is given to prove that the triangles are congruent. If so, state the theorem you would use.

△XYZ, △JKL

• yes; SAS Congruence Theorem

• yes; AAS Congruence Theorem

• yes; SSA Congruence Theorem

• No

Answer explanation

SSA is not one of the congruence theorems.

Decide whether enough information is given to prove that the triangles are congruent. If so, state the theorem you would use.

△RSV, △UTV

• yes; ASA Congruence

• yes; AAS Congruence

• yes; SAS Congruence

• No

Answer explanation

∠SVR ≅ ∠TVU because they are vertical angles.

Are these triangles congruent?

• Yes, by SSS
• Yes, by SAS
• Yes, by ASA
• No, this is the SSA one!!

Are these triangles congruent?

• Yes, by AAS
• Yes, by SAS
• Yes, by ASA
• No, this is the SSA one!!

Are these triangles congruent? If so, state the rule which you used to determine congruence.

• Yes by ASA
• Yes by AAS
• Yes by SSA
• Not congruent

Are these triangles congruent? If so, state the rule which you used to determine congruence.

• SSA
• AAS
• ASA
• Not necessarily congruent

Are the triangles congruent?

• Yes, by AAS

• Yes, by AA

• Yes, by ASA

• Yes, by SAS

• Not enough information

Are the triangles congruent?

• Yes, by SSA

• Yes, by SAS

• Yes, by SSS

• Not enough information