Question
It is given that quadrilateral QRST is a parallelogram. Which segment of the figure must be congruent to segment SP¯¯¯¯¯¯¯ ? (1 point) Responses PR¯¯¯¯¯¯¯¯ upper P upper R QS¯¯¯¯¯¯¯ upper Q upper S QP¯¯¯¯¯¯¯¯ upper Q upper P PT¯¯¯¯¯¯¯ upper P upper T Skip to navigation
Answers
GPT-4o mini
In a parallelogram, opposite sides are congruent. Since QRST is a parallelogram, we have the following pairs of congruent segments:
- QR ≅ ST
- QS ≅ RT
Given the segment SP, we need to determine which segment is congruent to it. In a parallelogram, the segments between the vertices will maintain their proportional lengths based on the properties of parallel lines.
The segment SP is congruent to segment QT, because in a parallelogram, the diagonals bisect each other. However, since QT is not listed as an option, we look for the congruent segment from the provided choices that could potentially connect with SP through the properties of a parallelogram.
From the options given:
- PR
- QS
- QP
- PT
Since none of the provided answers directly mention QT for the segment congruent to SP, and considering the properties of the parallelogram which focus on opposite sides, the one that is directly congruent (based on vertically opposite angles and similar triangles formed by diagonal intersections) is:
**QS (segment QS would be congruent to segment SP).**
So, the answer is:
**QS¯¯¯ (segment QS)**.
- QR ≅ ST
- QS ≅ RT
Given the segment SP, we need to determine which segment is congruent to it. In a parallelogram, the segments between the vertices will maintain their proportional lengths based on the properties of parallel lines.
The segment SP is congruent to segment QT, because in a parallelogram, the diagonals bisect each other. However, since QT is not listed as an option, we look for the congruent segment from the provided choices that could potentially connect with SP through the properties of a parallelogram.
From the options given:
- PR
- QS
- QP
- PT
Since none of the provided answers directly mention QT for the segment congruent to SP, and considering the properties of the parallelogram which focus on opposite sides, the one that is directly congruent (based on vertically opposite angles and similar triangles formed by diagonal intersections) is:
**QS (segment QS would be congruent to segment SP).**
So, the answer is:
**QS¯¯¯ (segment QS)**.