Question

The mapping of DEFG to D'E'F'G' is shown. 2 parallelograms have identical side lengths and angle measures. The second parallelogram is a reflection of the first. Which statements are true regarding the transformation? Check all that apply. EF corresponds to E'F'. FG corresponds to G'D'. ∠EDG Is-congruent-to ∠E'D'G' ∠DEF Is-congruent-to ∠D'E'F' The transformation is not isometric. The transformation is a rigid transformation.

Answer 1

In the given mapping, EF corresponds to E'F', ∠DEF is congruent to ∠D'E'F', and the transformation is a rigid transformation.

Step-by-step explanation:

The given mapping from DEFG to D'E'F' shows that the two parallelograms have identical side lengths and angle measures. The second parallelogram is a reflection of the first. Based on this information, we can determine which statements are true:

1. EF corresponds to E'F'. (True)
2. FG corresponds to G'D'. (False)
3. ∠EDG is congruent to ∠E'D'G'. (False)
4. ∠DEF is congruent to ∠D'E'F'. (True)
5. The transformation is not isometric. (False)
6. The transformation is a rigid transformation. (True)

Answer 2

(A)EF corresponds to E'F'

(C)∠EDG Is-congruent-to ∠E'D'G'

(D)∠DEF Is-congruent-to ∠D'E'F'

(F)The transformation is a rigid transformation.

Step-by-step explanation:

Given:

• Parallelogram DEFG is mapped to D'E'F'G'
• DEFG and D'E'F'G' have identical side lengths and angle measures.

The following applies:

• EF corresponds to E'F'
• ∠EDG Is-congruent-to ∠E'D'G'
• ∠DEF Is-congruent-to ∠D'E'F'

Now, a rigid transformation is a transformation of the plane that preserves length. Since the two parallelograms have identical side lengths:

• The transformation is a rigid transformation.

Note that a reflection is an isometric transformation. Therefore the statement "The transformation is not isometric" is INCORRECT.

FG and GD are adjacent sides, therefore they may not necessarily be congruent. Thus FG does not corresponds to G'D'