Triangle Congruence Theorems

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem stating that if three sides of one triangle are equal to 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 stating that if two angles and the side between them in one triangle are equal to two angles and the side between them in 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 stating that 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

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem stating that if two sides and the angle between them in one triangle are equal to two sides and the angle between them in another triangle, then the triangles are congruent.

Front

What is the significance of the SSA condition in triangle congruence?

Back

SSA (Side-Side-Angle) does not guarantee triangle congruence because it can lead to ambiguous cases where two different triangles can be formed.

Front

How do you denote congruent triangles?

Back

Congruent triangles are denoted using the symbol '≅'. For example, if triangle ABC is congruent to triangle DEF, it is written as triangle ABC ≅ triangle DEF.

Front

If triangle XYZ is congruent to triangle XWZ, how do you name the corresponding angles?

Back

If triangle XYZ is congruent to triangle XWZ, then angle X corresponds to angle X, angle Y corresponds to angle W, and angle Z corresponds to angle Z.

Front

What additional information is needed to prove two triangles are congruent by ASA?

Back

To prove two triangles are congruent by ASA, you need to show that two angles and the included side of one triangle are equal to two angles and the included side of the other triangle.

Front

What is the relationship between the sides of congruent triangles?

Back

In congruent triangles, all corresponding sides are equal in length.

Front

What is the relationship between the angles of congruent triangles?

Back

In congruent triangles, all corresponding angles are equal in measure.