Question

Given paralleogram ABCD≅parallelogram EFGH, which congruency statement is true?

Responses

BC¯¯¯¯¯≅GH¯¯¯¯¯¯
segment B C is congruent to segment G H

∠C≅∠G
angle C is congruent to angle G

∠B≅∠E
angle B is congruent to angle E

AD¯¯¯¯¯≅EF¯¯¯¯¯

Answer 1

In the case of congruent parallelograms, corresponding sides and angles are congruent. Given the statement that parallelogram ABCD is congruent to parallelogram EFGH, we can deduce the following congruencies:

1. Corresponding sides are congruent:
- AB ≅ EF
- BC ≅ FG
- CD ≅ GH
- DA ≅ HE

2. Corresponding angles are congruent:
- ∠A ≅ ∠E
- ∠B ≅ ∠F
- ∠C ≅ ∠G
- ∠D ≅ ∠H

Given the choices you provided, the valid congruency statements resulting from the congruence of the two parallelograms are:

- **BC ≅ GH** (this choice corresponds to the second option provided).
- **∠C ≅ ∠G** (this choice corresponds to the first option provided).
- **∠B ≅ ∠E** (this choice corresponds to the third option provided).
- **AD ≅ EF** (this choice corresponds to the last option provided).

Thus, **all the statements** you provided are true because they each reflect a valid congruency between the corresponding sides or angles of the two congruent parallelograms.