Congruent Figures

Front

What are congruent figures?

Back

Congruent figures are shapes that are identical in form and size. They can be superimposed on each other, meaning all corresponding sides and angles are equal.

Front

What does the symbol '≅' represent in geometry?

Back

The symbol '≅' denotes that two figures are congruent.

Front

If \( \Delta ABC \cong \Delta DEF \), what can we say about their corresponding sides and angles?

Back

The corresponding sides and angles of the triangles are equal: \( \overline{AB} \cong \overline{DE}, \overline{BC} \cong \overline{EF}, \overline{CA} \cong \overline{FD} \) and \( \angle A \cong \angle D, \angle B \cong \angle E, \angle C \cong \angle F \).

Front

How do you write a congruence statement for two triangles?

Back

A congruence statement lists the corresponding vertices of the triangles in order. For example, if \( \Delta ABC \cong \Delta DEF \), then A corresponds to D, B to E, and C to F.

Front

What is the importance of the order of vertices in congruence statements?

Back

The order of vertices is crucial because it indicates which angles and sides correspond to each other. Incorrect order can lead to wrong conclusions about congruence.

Front

If \( \overline{AB} \cong \overline{CD} \) and \( \overline{BC} \cong \overline{DE} \), what can we infer about triangles \( \Delta ABC \) and \( \Delta CDE \)?

Back

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 by the Side-Angle-Side (SAS) postulate.

Front

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

Back

The SSS Congruence Postulate states that 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

The ASA Congruence Postulate states that 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

If two triangles are congruent, what can we say about their areas?

Back

If two triangles are congruent, their areas are equal.

Front

What is the relationship between corresponding angles in congruent triangles?

Back

In congruent triangles, all corresponding angles are equal.