Geometry - AAS, SAS, SSS, ASA

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem that states if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem that states if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem that states if two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the triangles are congruent.

Front

What is the congruence statement for triangles ABC and DEF if

Back

The congruence statement is ABC ≅ DEF by ASA.

Front

If two triangles have two pairs of congruent angles, what can be concluded about the triangles?

Back

The triangles are congruent by the AAS or ASA theorem.

Front

If triangle XYZ is congruent to triangle PQR, what can be said about their corresponding sides and angles?

Back

The corresponding sides and angles of triangle XYZ and triangle PQR are congruent.

Front

What is the significance of the included angle in the SAS theorem?

Back

The included angle is the angle formed between the two sides being compared; it is crucial for establishing congruence in the SAS theorem.

Front

Can two triangles be congruent if only two sides are known to be equal?

Back

No, two triangles cannot be concluded as congruent with only two sides known; additional information such as an angle is needed.

Front

What is the difference between AAS and ASA?

Back

AAS involves two angles and a non-included side, while ASA involves two angles and the included side.