Nate rotates trapezoid WXYZ by 90° clockwise to produce ABCD. In WXYZ, sides WX and YZ are parallel, $m\angle W=90^\circ$, $WX=12$, $YZ=5$, and $m\angle X=50^\circ$.

Select all of the true statements.

Question

07-05-2025
Mathematics

High School

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Nate rotates trapezoid WXYZ by 90° clockwise to produce ABCD. In WXYZ, sides WX and YZ are parallel, $m\angle W=90^\circ$, $WX=12$, $YZ=5$, and $m\angle X=50^\circ$.

Select all of the true statements.

Answer :

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AlbertFrancis AlbertFrancis · Answer 1 · 2024-08-14T09:10:24-04:00

The true statements concerning the rotation of trapezoid WXYZ to form ABCD are that the lengths of corresponding sides and the measure of angles remain unchanged, and parallelism is preserved in the rotated figure.

The question discusses a geometric transformation where a trapezoid WXYZ is rotated 90° clockwise to produce a new figure ABCD. We are given that WX and YZ are parallel sides of the original trapezoid, with WX being 12 units in length and YZ being 5 units in length. Also, the original trapezoid has a right angle at W (m∠W=90°) and m∠X=50°.

Following the principles of geometric rotation, true statements about this scenario include that the lengths of corresponding sides on the original and rotated figures remain the same (thus, if WX=12 then its corresponding side in ABCD also measures 12 units), angles remain the same (thus if m∠W is 90° in WXYZ, then its corresponding angle in ABCD will also be 90° after rotation), and parallelism is preserved (thus if WX is parallel to YZ in WXYZ, then their corresponding sides in ABCD will also be parallel).

It's important to visualize the rotation and consider the properties that remain invariant during such a geometric transformation like distances, angles, and parallelism.

Nate rotates trapezoid WXYZ by 90° clockwise to produce ABCD. In WXYZ, sides WX and YZ are parallel, \(m\angle W=90^\circ\), \(WX=12\), \(YZ=5\), and \(m\angle X=50^\circ\).Select all of the true statements.

Answer :

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Nate rotates trapezoid WXYZ by 90° clockwise to produce ABCD. In WXYZ, sides WX and YZ are parallel, \(m\angle W=90^\circ\), \(WX=12\), \(YZ=5\), and \(m\angle X=50^\circ\).

Select all of the true statements.