HG 3.1 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 '≅' indicates that two figures are congruent.

Front

How can you determine if two triangles are congruent?

Back

Two triangles are congruent if their corresponding sides and angles are equal. This can be established using congruence postulates such as SSS (Side-Side-Side), SAS (Side-Angle-Side), and ASA (Angle-Side-Angle).

Front

What is the SSS Congruence Postulate?

Back

The SSS (Side-Side-Side) 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 SAS Congruence Postulate?

Back

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

Front

What is the ASA Congruence Postulate?

Back

The ASA (Angle-Side-Angle) 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

What is the AAS Congruence Theorem?

Back

The AAS (Angle-Angle-Side) Congruence Theorem states that 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 HL Congruence Theorem?

Back

The HL (Hypotenuse-Leg) Congruence Theorem states that 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 write a congruence statement for triangles?

Back

A congruence statement lists the corresponding vertices of the congruent triangles in the same order. For example, if triangle ABC is congruent to triangle DEF, it is written as ΔABC ≅ ΔDEF.

Front

What is the importance of corresponding parts in congruent figures?

Back

Corresponding parts of congruent figures are important because they help establish the congruence of the figures. If two figures are congruent, all corresponding sides and angles are equal.