Triangle Congruence

Front

What is the definition of triangle congruence?

Back

Triangle congruence means that two triangles are congruent if they have the same size and shape, which can be proven using various congruence theorems.

Front

What are the main triangle congruence theorems?

Back

The main triangle congruence theorems are SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and HL (Hypotenuse-Leg for right triangles).

Front

What does the SSS theorem state?

Back

The SSS (Side-Side-Side) theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Front

What does the SAS theorem state?

Back

The SAS (Side-Angle-Side) theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Front

What does the ASA theorem state?

Back

The ASA (Angle-Side-Angle) theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Front

What does the AAS theorem state?

Back

The AAS (Angle-Angle-Side) theorem states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What does the HL theorem state?

Back

The HL (Hypotenuse-Leg) theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What is the significance of corresponding parts of congruent triangles?

Back

Corresponding parts of congruent triangles are congruent, meaning that if two triangles are proven to be congruent, all their corresponding sides and angles are also congruent.

Front

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

Back

To determine if two triangles are congruent using the SSS theorem, measure the lengths of all three sides of both triangles and check if they are equal.

Front

What is the relationship between triangle congruence and similarity?

Back

Triangle congruence means that triangles are the same size and shape, while triangle similarity means that triangles have the same shape but may differ in size.