Triangle Congruence Theorems

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 equal to two angles and the included side 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 three sides of one triangle are equal to three sides 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 equal to two sides and the included angle of another triangle, then the triangles are congruent.

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 equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

Which triangle congruence theorem is NOT valid?

Back

AAA (Angle-Angle-Angle) is not a valid triangle congruence theorem because it does not guarantee that the triangles are congruent; it only shows that they are similar.

Front

If two triangles have two pairs of equal angles, what can be concluded?

Back

The triangles are similar, but not necessarily congruent unless the corresponding sides are also equal.

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 one side and two angles are known?

Back

Yes, if the known side is included between the two known angles, the triangles can be proven congruent using the ASA theorem.

Front

What is the relationship between congruence and similarity in triangles?

Back

All congruent triangles are similar, but not all similar triangles are congruent. Congruent triangles have the same size and shape, while similar triangles have the same shape but may differ in size.

Front

How can you prove triangles are congruent using the SSS theorem?

Back

By showing that all three corresponding sides of one triangle are equal to the three corresponding sides of another triangle.