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 symbol \( \cong \) represent in geometry?

Back

It denotes that two figures are congruent.

Front

If \( \Delta ABC \cong \Delta DEF \), what can be inferred about their corresponding angles?

Back

\( m\angle A = m\angle D \), \( m\angle B = m\angle E \), and \( m\angle C = m\angle F \).

Front

If two triangles are congruent, what can be said about their corresponding sides?

Back

Their corresponding sides are equal in length.

Front

What is the Side-Side-Side (SSS) Congruence Postulate?

Back

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

Front

What is the Angle-Side-Angle (ASA) Congruence Postulate?

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 is the Angle-Angle-Side (AAS) Congruence Theorem?

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 Hypotenuse-Leg (HL) Theorem for right triangles?

Back

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

How do you denote the congruence of triangles in a statement?

Back

By writing the triangle names in order of corresponding vertices, e.g., \( \Delta ABC \cong \Delta DEF \).

Front

What is the purpose of using congruence statements in geometry?

Back

To show that two triangles are identical in shape and size, allowing for the transfer of properties from one triangle to another.