Question

lesson 19: construct and apply a sequence of rigid motions
exit ticket
assuming that the following figures are drawn to scale. use your understanding of congruence to explain why square abcd and rhombus ghij are not congruent.

Explanation:

To determine congruence, rigid motions (translation, rotation, reflection) must map one figure to the other. Square \(ABCD\) has right angles (\(90^\circ\)), while rhombus \(GHIJ\) has non - right angles. Rigid motions preserve angle measures. Since the angle measures of the square and the rhombus differ, no sequence of rigid motions can map the square to the rhombus, so they are not congruent.

Answer:

Square \(ABCD\) and rhombus \(GHIJ\) are not congruent because rigid motions (which preserve angle measures) cannot map the square (with right angles) to the rhombus (with non - right angles) as their angle measures differ.