Question

is δwxy congruent to δjkl? justify your answer using rigid motions. yes. a rotation and a dilation can map δwxy onto δjkl. yes. a translation and a rotation can map δwxy onto δjkl. no. it is not possible to map δwxy onto δjkl using only rigid motions.

Explanation:

Step1: Recall Rigid Motions

Rigid motions (translation, rotation, reflection) preserve side lengths and angles. Check if corresponding sides/angles of \( \triangle WXY \) and \( \triangle JKL \) are equal.

• Sides: \( WY = 6 \) in, \( XY = 4 \) in, \( WX = 7 \) in; \( LJ = 6 \) in, \( KL = 4 \) in, \( KJ = 7 \) in.
• Angles: Corresponding angles (e.g., \( \angle Y = 86.4^\circ \), \( \angle L = 86.4^\circ \); \( \angle X = 58.8^\circ \), \( \angle K = 58.8^\circ \); \( \angle W = 34.8^\circ \), \( \angle J = 34.8^\circ \)) are equal.

Step2: Analyze Transformations

Since sides/angles match, rigid motions (translation to move, rotation to align) can map \( \triangle WXY \) to \( \triangle JKL \). Dilation is not rigid (changes size), but here sizes are equal, so translation + rotation (both rigid) work.

Answer:

Yes. A translation and a rotation can map \( \triangle WXY \) onto \( \triangle JKL \).