Congruent Triangles and Their Properties

Front

What are congruent triangles?

Back

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

Front

What is the symbol for congruence?

Back

The symbol for congruence is '≅'.

Front

What does the Side-Side-Side (SSS) Congruence Postulate 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 Angle-Side-Angle (ASA) Congruence Postulate 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 Side-Angle-Side (SAS) Congruence Postulate 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 Angle-Angle (AA) Similarity Postulate imply about triangles?

Back

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar, but not necessarily congruent.

Front

How can you determine if two triangles are congruent using the Hypotenuse-Leg (HL) 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 a congruence statement?

Back

A statement that indicates that two figures are congruent, listing corresponding parts in the same order.

Front

If ∆ABC ≅ ∆DEF, what can be inferred about their corresponding parts?

Back

Angle A = Angle D, Angle B = Angle E, Angle C = Angle F, Side AB = Side DE, Side BC = Side EF, Side AC = Side DF.

Front

What is the importance of congruence in geometry?

Back

Congruence helps in proving that two shapes are identical in form, which is essential for solving problems related to shape and size.