B. A, B, and E

UpStudy Free Solution:

If two or more polygons are congruent, several specific properties must be true about the polygons. Let's analyze each of the statements given in the choices:

A. Pairs of corresponding angles have the same measure.

B. Pairs of corresponding sides have the same length.

C. The polygons are parallelograms.

D. The polygons are regular.

E. Rigid transformations can be used to map one polygon onto the other.

For two polygons to be congruent:

1. Corresponding angles must be equal (statement A).

2. Corresponding sides must have the same length (statement B).

3. Rigid transformations (such as translation, rotation, and reflection) can be used to map one polygon onto the other (statement E).

However, for polygons to be congruent, they do not necessarily need to be parallelograms (statement C) or regular polygons (statement D). These are specific types of polygons, but congruence can apply to any type of polygon as long as the corresponding angles and sides are equal and a rigid transformation can map one onto the other.

Therefore, the correct choice must include statements A, B, and E, but not C or D.

Key Concepts:

1. Congruent Polygons: Two polygons are congruent if they have the same shape and size, which means their corresponding angles and sides are equal.

2. Rigid Transformations: These include translations, rotations, and reflections. Rigid transformations do not change the size or shape of a polygon.

Explanation:

- Corresponding Angles: For two polygons to be congruent, all pairs of corresponding angles must have the same measure. This ensures that the polygons have the same shape.

- Statement A: True. Corresponding angles must be equal.

- Corresponding Sides: In congruent polygons, all pairs of corresponding sides must have the same length. This ensures that the polygons have the same size.

- Statement B: True. Corresponding sides must be equal.

- Rigid Transformations: Congruent polygons can be mapped onto each other using rigid transformations (translation, rotation, reflection), which preserve the size and shape.

- Statement E: True. Rigid transformations can map one polygon onto the other.

- Parallelograms: While some congruent polygons may be parallelograms, this is not a necessary condition for congruence. Congruence can apply to any polygon type.

- Statement C: False. Polygons do not need to be parallelograms to be congruent.

- Regular Polygons: Similarly, congruent polygons do not need to be regular (all sides and angles equal). Congruence can apply to any polygons with equal corresponding sides and angles.

- Statement D: False. Polygons do not need to be regular to be congruent.

For two polygons to be congruent, they must satisfy the conditions in statements A, B, and E. They do not need to be parallelograms or regular polygons.

Knowledge about the properties of congruent polygons makes it possible to solve a variety of geometric problems. Solve the present issues and the similar problems listed above using UpStudy geometry solver, receiving detailed step-by-step solutions. UpStudy has much more to offer than an ordinary key. It explains each topic in detail. Go ahead and get a good knowledge of various issues.