geom 7.1B flashcard

Front

What is a congruence statement in geometry?

Back

A congruence statement indicates that two geometric figures are congruent, meaning they have the same shape and size. It is often written using the symbol '≅'. For example, if triangle ABC is congruent to triangle DEF, it is written as ΔABC ≅ ΔDEF.

Front

What does the symbol '≅' represent?

Back

The symbol '≅' represents congruence in geometry, indicating that two figures are congruent in shape and size.

Front

How do you determine if two triangles are congruent?

Back

Two triangles can be determined to be congruent using several criteria: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL) for right triangles.

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 two triangles are congruent.

Front

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

Back

The SAS 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 two 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 two triangles are congruent.

Front

What is the Angle-Angle-Side (AAS) Congruence Theorem?

Back

The AAS 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 two triangles are congruent.

Front

What is the Hypotenuse-Leg (HL) Theorem?

Back

The HL 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 two triangles are congruent.

Front

What is the difference between congruence and similarity?

Back

Congruence means that two figures are the same size and shape, while similarity means that two figures have the same shape but may be different sizes.

Front

How can you write a congruence statement for two triangles?

Back

To write a congruence statement for two triangles, list the vertices of the triangles in corresponding order. For example, if triangle ABC is congruent to triangle DEF, it is written as ΔABC ≅ ΔDEF.