Congruent Triangles Methods

Which additional information is needed to provide the named triangles are congruent by the given method?

Answer explanation

A pair of angles and a pair of shared sides are marked congruent. The pair of angles to be congruent are angles M and C. This places the marked side NOT between the congruent angles to prove the triangles are congruent using AAS. (If angles MBA and CAB are congruent, that would be ASA.)

Consider if any additional information can be marked up in the given diagram. Then determine if the pair of triangles can be proved congruent by SSS, SAS, ASA, or AAS. If the triangles cannot be proven congruent by one of those methods, choose "Not Congruent"

• SSS

• SAS

• ASA

• AAS

• NOT CONGRUENT

Answer explanation

Even though the vertical angles formed by the intersecting sides are congruent, there is no AAA method to prove triangles congruent. The triangles CANNOT be proven congruent!

Consider if any additional information can be marked up in the given diagram. Then determine if the pair of triangles can be proved congruent by SSS, SAS, ASA, or AAS. If the triangles cannot be proven congruent by one of those methods, choose "Not Congruent"

• SSS

• SAS

• ASA

• AAS

• NOT CONGRUENT

Answer explanation

The shared side AC is congruent in both triangles by refleXive , so the triangles are congruent by ASA.

Consider if any additional information can be marked up in the given diagram. Then determine if the pair of triangles can be proved congruent by SSS, SAS, ASA, or AAS. If the triangles cannot be proven congruent by one of those methods, choose "Not Congruent"

• SSS

• SAS

• ASA

• AAS

• NOT CONGRUENT

Answer explanation

The shared side AC is congruent in both triangles by refleXive , so the triangles are congruent by AAS. Notice that this is NOT ASA because the side between the marked congruent angles is NOT marked congruent!!

Consider if any additional information can be marked up in the given diagram. Then determine if the pair of triangles can be proved congruent by SSS, SAS, ASA, or AAS. If the triangles cannot be proven congruent by one of those methods, choose "Not Congruent"

• SSS

• SAS

• ASA

• AAS

• NOT CONGRUENT

Answer explanation

Even though the vertical angles can be proven congruent, SSA does NOT prove triangles congruent (unless the A is a right angle and then we have HL!) so the triangles canNOT be proven congruent.

Consider if any additional information can be marked up in the given diagram. Then determine if the pair of triangles can be proved congruent by SSS, SAS, ASA, or AAS. If the triangles cannot be proven congruent by one of those methods, choose "Not Congruent"

• SSS

• SAS

• ASA

• AAS

• NOT CONGRUENT

Answer explanation

The shared side, PR, is congruent in both triangles by refleXive, so the triangles are congruent by SSS.

Consider if any additional information can be marked up in the given diagram. Then determine if the pair of triangles can be proved congruent by SSS, SAS, ASA, or AAS. If the triangles cannot be proven congruent by one of those methods, choose "Not Congruent"

• SSS

• SAS

• ASA

• AAS

• NOT CONGRUENT

Answer explanation

The shared side, MK, is congruent in both triangles by refleXive, so the triangles are congruent by SAS. (Remember, MK is called a diagonal of that quadrilateral.)

Which additional information is needed to provide the named triangles are congruent by the given method?

Answer explanation

Two pairs of sides are marked congruent, so we need the remaining pair of sides, NG and NM to be congruent to prove the triangles are congruent using SSS.

Which additional information is needed to provide the named triangles are congruent by the given method?

Answer explanation

A pair of angles and a pair of sides are marked congruent. The remaining pair of angles to be congruent are angles S and H to prove the triangles are congruent using AAS. (If angles SUT and HUT are congruent, that would be ASA.)

Which additional information is needed to provide the named triangles are congruent by the given method?

Answer explanation

A pair of angles are marked congruent. The pair of sides to be congruent are sides LV and VU (the sides included between the marked angles) to prove the triangles are congruent using ASA. (If sides LN and UW or NV and VU are congruent, that would be AAS.)