Congruent Triangles

Front

What are congruent triangles?

Back

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

Front

What does the SSS congruence 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 congruence 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 congruence 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 congruence theorem state?

Back

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

Front

What is the HL theorem?

Back

The Hypotenuse-Leg (HL) 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 triangles are congruent.

Front

What is the difference between congruence and similarity in triangles?

Back

Congruent triangles are identical in size and shape, while similar triangles have the same shape but may differ in size.

Front

How can you prove triangles are congruent using the SSS theorem?

Back

Measure the lengths of all three sides of both triangles and show that they are equal.

Front

How can you prove triangles are congruent using the SAS theorem?

Back

Measure two sides and the included angle of both triangles and show that they are equal.

Front

What is a congruence statement?

Back

A statement that indicates two triangles are congruent, typically written as ΔABC ≅ ΔDEF.