Triangle Congruence Theorems

Front

What is the definition of congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the SAS (Side-Angle-Side) 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 (Angle-Side-Angle) 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 SSS (Side-Side-Side) theorem state?

Back

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

Front

What does the AAS (Angle-Angle-Side) theorem state?

Back

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 is the HL (Hypotenuse-Leg) theorem?

Back

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

Front

What is the significance of corresponding parts in congruent triangles?

Back

In congruent triangles, corresponding parts (sides and angles) are equal, which helps in proving triangle congruence.

Front

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

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 the SAS theorem?

Back

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

Front

What is the difference between ASA and AAS?

Back

ASA requires the included side between two angles to be known, while AAS does not require the side to be between the two angles.