Congruent Figures and Triangles

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 it mean for triangles to be congruent?

Back

Triangles are congruent if all three sides and all three angles of one triangle are equal to the corresponding sides and angles of another triangle.

Front

What is the symbol for congruence?

Back

The symbol for congruence is '≅'.

Front

List the criteria for triangle congruence.

Back

1. Side-Side-Side (SSS) Congruence 2. Side-Angle-Side (SAS) Congruence 3. Angle-Side-Angle (ASA) Congruence 4. Angle-Angle-Side (AAS) Congruence 5. Hypotenuse-Leg (HL) Congruence (for right triangles)

Front

If ΔXYZ ≅ ΔCAB, what can be said about their corresponding parts?

Back

The corresponding parts of congruent triangles are equal. Therefore, ∠X ≅ ∠C, ∠Y ≅ ∠A, ∠Z ≅ ∠B, and XY ≅ CA, YZ ≅ AB, XZ ≅ CB.

Front

What does the term 'corresponding parts' refer to in congruent triangles?

Back

Corresponding parts refer to the sides and angles of congruent triangles that match each other in position and measure.

Front

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

Back

If two triangles are congruent, their areas are equal.

Front

What is the relationship between the angles of congruent triangles?

Back

In congruent triangles, all corresponding angles are equal.

Front

What is the definition of corresponding sides in congruent triangles?

Back

Corresponding sides are the sides of two triangles that are in the same relative position.

Front

If ∠A ≅ ∠D, what can be inferred about triangles that are congruent?

Back

If ∠A ≅ ∠D, then the triangles are congruent, meaning all corresponding parts are equal.