Triangle Congruence Shortcuts

Front

What does ASA stand for in triangle congruence?

Back

Angle-Side-Angle: A triangle is congruent if two angles and the included side are equal to two angles and the included side of another triangle.

Front

What does AAS stand for in triangle congruence?

Back

Angle-Angle-Side: A triangle is congruent if two angles and a non-included side are equal to two angles and a corresponding non-included side of another triangle.

Front

What does SAS stand for in triangle congruence?

Back

Side-Angle-Side: A triangle is congruent if two sides and the included angle are equal to two sides and the included angle of another triangle.

Front

What does SSS stand for in triangle congruence?

Back

Side-Side-Side: A triangle is congruent if all three sides are equal to the corresponding sides of another triangle.

Front

Can two triangles be congruent if only one side is known?

Back

No, at least two sides and the included angle or two angles and the included side must be known.

Front

If ΔABE ≅ ΔCDE by AAS, what can be inferred about their angles and sides?

Back

The two angles and the non-included side of ΔABE are equal to the corresponding angles and side of ΔCDE.

Front

What is the significance of the order of letters in triangle congruence?

Back

The order of letters indicates the corresponding vertices of the triangles that are congruent.

Front

If ΔABC ≅ ΔDEF by SAS, what does this imply about the triangles?

Back

The two sides and the included angle of ΔABC are equal to the corresponding two sides and included angle of ΔDEF.

Front

What is the difference between SSA and other congruence criteria?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases.

Front

What is the first step in proving triangle congruence?

Back

Identify the known sides and angles of the triangles in question.