Question

triangle congruence: asa and aas
two rigid transformations are used to map \\( \triangle jkl \\) to \\( \triangle mnq \\). the first is a translation of vertex \\( l \\) to vertex \\( q \\). what is the second transformation?

• a rotation about point \\( k \\)
• a reflection across the line containing \\( \overline{jk} \\)
• a reflection across the line containing \\( \overline{lk} \\)
• a rotation about point \\( l \\)

Explanation:

Rigid transformations include translation, rotation, and reflection. After translating vertex \(L\) to vertex \(Q\), we need to align the other vertices and angles. A rotation about point \(L\) (since \(L\) is already translated to \(Q\) in the first step) will help map the remaining parts of \(\triangle JKL\) to \(\triangle MNQ\). Rotation about a point changes the orientation of the figure while keeping distances and angles (rigid property). A rotation about point \(K\) would not be correct as \(L\) is the vertex that was first translated. Reflections across lines \(\overline{JK}\) or \(\overline{LK}\) would change the position in a non - rotational (flipping) way which is not suitable here as we are dealing with mapping one triangle to another with a sequence of rigid motions where the first is a translation of \(L\) to \(Q\).

Answer:

a rotation about point \(L\)