Question

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

Explanation:

Step1: Use congruence of angles

Since \(\angle E\cong\angle H\), we want to align these angles.

Step2: Use the congruence of sides

We know that \(\overline{EK}\cong\overline{LH}\). When we rotate \(\triangle HLA\) (a congruence transformation that preserves shape and size), we want to make the sides and angles match. Since \(\angle E\) and \(\angle H\) are congruent, we rotate \(\triangle HLA\) so that point \(E\) and point \(H\) coincide (because the angles at \(E\) and \(H\) are congruent and we want to start the alignment from these vertices for the ASA (angle - side - angle) verification). Also, because \(\overline{EK}\cong\overline{LH}\), after rotating \(\triangle HLA\) so that \(E\) and \(H\) coincide, the side \(EK\) (of \(\triangle EKS\)) and \(LH\) (of \(\triangle HLA\)) will be in a position to check the other pair of congruent angles.

Step3: Use the other pair of congruent angles

Since \(\angle K\cong\angle L\), after the rotation (which preserves angles), the two triangles \(\triangle EKS\) and \(\triangle HLA\) will overlap completely (by the ASA postulate: if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent).

Answer:

\(H\)