Question

Use the image to answer the question.

Parallelogram upper S upper T upper U upper V is shown with base upper U upper V larger than height upper T upper U. Diagonals are drawn from upper S to upper U and upper T to upper V to meet at upper R.

Which statement must be true of parallelogram STUV
?

(1 point)
Responses which answer is correct and why

VT¯¯¯¯¯¯¯
must be congruent to SU¯¯¯¯¯¯¯
.
line segment cap v cap t must be congruent to line segment cap s cap u. - incorrect

ST¯¯¯¯¯¯¯
must be congruent to TU¯¯¯¯¯¯¯
.
line segment cap s cap t must be congruent to line segment cap t cap u. - no response given

SR¯¯¯¯¯¯¯
must be congruent to RT¯¯¯¯¯¯¯
.
line segment cap s cap r must be congruent to line segment cap r cap t. - no response given

SR¯¯¯¯¯¯¯
must be congruent to UR¯¯¯¯¯¯¯¯
.
line segment cap s cap r must be congruent to line segment cap u cap r. - no response given
Incorrect

This statement is true only if STUV is a rectangle in addition to being a parallelogram.
Remaining Attempts : 1
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Answer 1

To determine which statement must be true of the parallelogram STUV, we should analyze the properties of a parallelogram.

1. **Opposite sides are congruent:** In any parallelogram, the opposite sides are equal in length. Hence, \( ST \) is congruent to \( UV \), and \( SU \) is congruent to \( TV \).

2. **Diagonals bisect each other:** The diagonals of a parallelogram bisect each other, which means that the segments formed by the intersection of the diagonals are equal.

Now let's evaluate each statement provided:

1. **\( VT \) must be congruent to \( SU \)**: This is incorrect in general; this would only be true if STUV is a rectangle.

2. **Line segment \( VT \) must be congruent to line segment \( SU \)**: This is also incorrect because these segments are not opposite sides of the parallelogram.

3. **\( ST \) must be congruent to \( TU \)**: This is incorrect, as these are adjacent sides, not opposite sides.

4. **\( SR \) must be congruent to \( RT \)**: This statement is true based on the property of the diagonals bisecting each other. Since \( R \) is the point where the diagonals intersect, \( SR \) is equal to \( RT \).

5. **\( SR \) must be congruent to \( UR \)**: This is incorrect because these segments are not the bisected halves of the same diagonal.

Therefore, the correct statement is:
- **\( SR \) must be congruent to \( RT \) (correct answer)**, based on the property that the diagonals of a parallelogram bisect each other.