Question

describe a composition of rigid motions that maps de to jk and ∠d to ∠j. why doesnt this composition show that there is no angle - side - side congruence criterion? translate point d onto point ▼ then ▼ △def about point ▼ such that point e lies on point ▼ even though ef≅kl, point f will not map to point ▼ so angle - side - side is not sufficient to prove the triangles congruent.

Explanation:

Step1: First translation

Translate point D onto point J. This is the first - step of the rigid - motion composition. It aligns one vertex of the two triangles.

Step2: Rotation about point

Then rotate $\triangle DEF$ about point D (now on J) such that point E lies on point K. This step aligns one side of the two triangles.

Step3: Analyze congruence

Even though $EF\cong KL$, point F will not map to point L. For the Side - Angle - Side (SAS) congruence criterion, we need two sides and the included angle to be congruent. Here, the mapping of the sides and angles does not satisfy the SAS criterion. So, the triangles are not congruent by SAS.

Answer:

The composition of rigid motions: First, translate point D onto point J. Then rotate $\triangle DEF$ about point D (now on J) such that point E lies on point K. Since point F does not map to point L even with $EF\cong KL$, the Side - Angle - Side congruence criterion is not met.