Triangle Congruency Theorems

Front

What does the SSS triangle congruency theorem state?

Back

If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

Front

What does the SAS triangle congruency theorem state?

Back

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 the ASA triangle congruency theorem state?

Back

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 the AAS triangle congruency theorem state?

Back

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

Front

What does the HL triangle congruency theorem state?

Back

If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the SSA condition in triangle congruency?

Back

SSA does not guarantee triangle congruency; it can lead to ambiguous cases.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means their corresponding sides and angles are equal.

Front

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

Back

Measure all three sides of both triangles; if all three pairs of sides are equal, the triangles are congruent.

Front

How can you determine if two triangles are congruent using SAS?

Back

Measure two sides and the included angle of both triangles; if they are equal, the triangles are congruent.

Front

How can you determine if two triangles are congruent using ASA?

Back

Measure two angles and the included side of both triangles; if they are equal, the triangles are congruent.