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 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 two angles and the included side of another triangle, the triangles are congruent.

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 two angles and the corresponding non-included side 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 two sides and the included angle of another triangle, the triangles are congruent.

Front

What does AA stand for in triangle congruence?

Back

AA stands for Angle-Angle, a rule that states if two angles of one triangle are equal to two angles of another triangle, the triangles are similar, but not necessarily congruent.

Front

What is SSA in triangle congruence?

Back

SSA stands for Side-Side-Angle, which is not a valid rule for proving triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

Front

How can you determine if two triangles are congruent using the SSS rule?

Back

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

Front

What is the significance of corresponding parts in triangle congruence?

Back

Corresponding parts are the sides and angles of triangles that match up when the triangles are congruent, meaning they have the same measure.

Front

If ∠A ≅ ∠D and ∠B ≅ ∠E, what can be concluded about triangles ABC and DEF?

Back

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar, but not necessarily congruent unless the third angles are also equal.

Front

What is the relationship between triangle similarity and congruence?

Back

All congruent triangles are similar, but not all similar triangles are congruent. Congruent triangles have equal corresponding sides and angles, while similar triangles have proportional sides and equal corresponding angles.