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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.