Congruent Triangles

Front

What are congruent triangles?

Back

Congruent triangles are triangles that are identical in shape and size, meaning their corresponding sides and angles are equal.

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

Front

What additional information is needed to prove triangles are congruent using the HL theorem?

Back

To use the HL theorem, you need to know that both triangles are right triangles and that the lengths of their hypotenuses and one leg are equal.

Front

What does the SSS theorem state?

Back

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

Front

What is the SAS theorem?

Back

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

Front

What is the ASA theorem?

Back

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

Front

What is the AAS theorem?

Back

The AAS (Angle-Angle-Side) theorem states 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 two triangles are congruent.

Front

What is the definition of corresponding parts of congruent triangles?

Back

Corresponding parts of congruent triangles are the sides and angles that are in the same relative position in each triangle.

Front

How can you prove triangles are congruent using the properties of isosceles triangles?

Back

If two sides of a triangle are equal, the angles opposite those sides are also equal, which can help in proving congruence.

Front

What is the significance of the triangle inequality theorem in triangle congruence?

Back

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which is essential for determining the possibility of triangle congruence.