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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

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 analyze the statements about parallelogram STUV and the points defined in the question, we can use the properties of parallelograms and their diagonals.

In a parallelogram:

• Opposite sides are equal and parallel.
• Diagonals bisect each other.

Given that the diagonals from points S to U and T to V meet at point R, we can determine that SR is equal to RU and TR is equal to RV.

Let's evaluate each statement:

1. VT must be congruent to SU: This is not necessarily true for all parallelograms, as we can't conclude anything specific about these segments without additional information about the angles or side lengths.

2. ST must be congruent to TU: This is true for a parallelogram (opposite sides are equal). However, it may not hold if specific conditions (like it being a rectangle) are not met.

3. SR must be congruent to RT: This is not necessarily true. While R is the midpoint of both diagonals, this statement refers to segments that do not apply equally to all cases.

4. SR must be congruent to UR: Similarly, this is only specific to rectangles and is not generally true for all parallelograms.

Thus, the most accurate overarching statement in this scenario, while noting that the figures and properties mentioned apply, would be that in parallelogram STUV, ST must be congruent to TU, as this holds true due to the properties of the parallelogram regardless of it being a rectangle or not.