Congruence Statements

Front

What is a congruence statement?

Back

A congruence statement is a mathematical statement that indicates two geometric figures are congruent, meaning they have the same shape and size. It is often written in the form of \( \Delta ABC \cong \Delta XYZ \).

Front

If \( \Delta ABC \cong \Delta XYZ \), what can be inferred about the corresponding sides?

Back

The corresponding sides of the triangles are equal in length, meaning \( AB \cong XY \), \( BC \cong YZ \), and \( AC \cong XZ \).

Front

What does the symbol '≅' represent in geometry?

Back

The symbol '≅' represents congruence, indicating that two figures have the same shape and size.

Front

How can you determine if two angles are congruent?

Back

Two angles are congruent if they have the same measure, which can be shown using a congruence statement.

Front

What is the significance of the order of letters in a congruence statement?

Back

The order of letters in a congruence statement indicates the corresponding vertices of the congruent figures. For example, in \( \Delta ABC \cong \Delta XYZ \), angle A corresponds to angle X, angle B to angle Y, and angle C to angle Z.

Front

If \( AB \cong XY \) and \( BC \cong YZ \), what can be concluded about triangles \( \Delta ABC \) and \( \Delta XYZ \)?

Back

If both pairs of corresponding sides are congruent, then the triangles are congruent by the Side-Side-Side (SSS) congruence postulate.

Front

What is the Angle-Angle (AA) criterion for triangle congruence?

Back

The AA criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are congruent.

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion, but they do not have to be congruent.

Front

How can you express that angle F is congruent to angle G using a congruence statement?

Back

You can express this as \( \angle F \cong \angle G \).

Front

What is the Side-Angle-Side (SAS) congruence postulate?

Back

The SAS postulate states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle is also congruent, then the triangles are congruent.