Triangle Congruence

Front

What is Triangle Congruence?

Back

Triangle Congruence refers to the condition where two triangles are considered congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does AAS stand for in triangle congruence?

Back

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

Front

What does ASA stand for in triangle congruence?

Back

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

Front

What does SAS stand for in triangle congruence?

Back

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

Front

What does SSS stand for in triangle congruence?

Back

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

Front

What is the SSA condition in triangle congruence?

Back

SSA stands for Side-Side-Angle, which is not a valid condition for proving triangle congruence because it can lead to ambiguous cases.

Front

What is the AAA condition in triangle congruence?

Back

AAA stands for Angle-Angle-Angle, which indicates that triangles are similar but not necessarily congruent, as they can have different sizes.

Front

If ∠A ≅ ∠D, what can be inferred about triangles that include these angles?

Back

If ∠A ≅ ∠D, it indicates that the triangles may be congruent if other conditions (like sides) are also satisfied.

Front

What is the significance of corresponding parts in triangle congruence?

Back

Corresponding parts refer to the sides and angles of triangles that are matched to determine congruence; they must be equal for the triangles to be congruent.

Front

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

Back

No, knowing only one angle is not sufficient to prove congruence; at least two angles and the included side or two sides and the included angle must be known.