Question

triangle opq and triangle jkl are drawn below. if \\(\overline{op} \cong \overline{jk}\\), \\(\overline{pq} \cong \overline{kl}\\), and \\(\overline{oq} \cong \overline{jl}\\), use the dropdown boxes below to determine a sequence of two transformations that maps triangle opq onto triangle jkl. then use a congruence statement to explain why this is possible. image of triangles opq and jkl rotate triangle opq counterclockwise about point until has the same slope as. then triangle opq

Explanation:

Step1: Rotate triangle \(OPQ\)

Rotate triangle \(OPQ\) counter - clockwise about point \(O\) until \(\overline{OP}\) has the same slope as \(\overline{JK}\).

Step2: Translate the rotated triangle

Then translate triangle \(O'P'Q'\) so that it maps onto triangle \(JKL\).

Since \(\overline{OP}\cong\overline{JK}\), \(\overline{PQ}\cong\overline{KL}\), and \(\overline{OQ}\cong\overline{JL}\), by the Side - Side - Side (SSS) congruence criterion, \(\triangle OPQ\cong\triangle JKL\). Congruent triangles can be mapped onto each other using a sequence of rigid transformations (rotation and translation in this case).

Answer:

First, rotate triangle \(OPQ\) counter - clockwise about point \(O\) until \(\overline{OP}\) has the same slope as \(\overline{JK}\). Then translate triangle \(O'P'Q'\). The congruence statement is \(\triangle OPQ\cong\triangle JKL\) (by SSS), which means they can be mapped onto each other via rigid transformations.