Question

verify the asa postulate for triangle congruence by using congruence transformations.
given: \\( \overline { e k } \cong \overline { l h } \\)
prove: \\( \delta e k s \cong \delta h l a \\)
\\( \angle e \cong \angle h \\)
\\( \angle k \cong \angle l \\)
since \\( \angle e \cong \angle h \\), translate \\( \delta h l a \\) so that points e and h coincide.
next \\( \delta h l a \\) so that side hl overlaps side \\( \square \\).

Explanation:

Step1: Analyze the given congruent angles and sides

We know that \(\overline{EK}\cong\overline{LH}\), \(\angle E\cong\angle H\), and \(\angle K\cong\angle L\). The first step is to use the congruent angles \(\angle E\) and \(\angle H\) to start the transformation. Translating \(\triangle HLA\) so that \(E\) and \(H\) coincide is a good start because of the angle - congruence.

Step2: Determine the second transformation

Since \(\overline{EK}\cong\overline{LH}\), after translating \(\triangle HLA\) so that \(E\) and \(H\) coincide, we need to rotate \(\triangle HLA\). Rotating \(\triangle HLA\) will make side \(HL\) (which is congruent to \(EK\)) overlap side \(EK\).

Answer:

Rotate; \(EK\)