Congruence statements

Front

What is a congruence statement in geometry?

Back

A congruence statement is a mathematical statement that indicates that two geometric figures are congruent, meaning they have the same shape and size.

Front

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

Back

The corresponding angles are congruent, meaning \( \angle A \cong \angle D \), \( \angle B \cong \angle E \), and \( \angle C \cong \angle F \).

Front

What does it mean for two line segments to be congruent?

Back

Two line segments are congruent if they have the same length.

Front

How do you denote that two angles are congruent?

Back

Two angles are denoted as congruent using the symbol \( \cong \). For example, if \( \angle A \cong \angle B \), it means angle A is congruent to angle B.

Front

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

Back

The order of vertices in a congruence statement indicates which angles and sides correspond to each other. For example, in \( \Delta ABC \cong \Delta DEF \), \( A \) corresponds to \( D \), \( B \) to \( E \), and \( C \) to \( F \).

Front

What is the relationship between corresponding sides in congruent triangles?

Back

In congruent triangles, the corresponding sides are also congruent, meaning their lengths are equal.

Front

If \( \overline{CA} \cong \overline{FD} \), what can be inferred about the triangles involved?

Back

If \( \overline{CA} \cong \overline{FD} \), it indicates that the triangles are congruent and that these sides correspond to each other.

Front

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

Back

The SSS Congruence Postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Front

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

Back

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

Front

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

Back

The ASA Congruence Postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.