Question

Liam and Tehya are trying to determine whether δabc and δefd can be proven congruent through rigid motions. Liam says that δabc ≅ δefd because δabc can be reflected over the y-axis to create δefd. Tehya says that δabc ≅ δefd because δabc can be rotated 90° clockwise about the origin to create δdef. Who is correct?

Option 1: Liam only
Option 2: Tehya only
Option 3: Both Liam and Tehya
Option 4: Neither Liam nor Tehya

Answer 1

Liam is correct. Congruence can be proven through reflection and rotation motions. Option 1: Liam only.

Step-by-step explanation:

In this case, both Liam and Tehya are correct. Liam's reasoning is valid because congruence can be proven through reflection over the y-axis. In rigid motions (also known as isometries), congruence can be proven through translations, rotations, and reflections. Tehya's statement involves a rotation, and rotations are rigid motions, but the orientation of the shapes after a 90° clockwise rotation is not the same. Therefore, Tehya's reasoning is not correct.

Liam's statement involves a reflection over the y-axis, and reflections are also rigid motions. If a reflection over the y-axis can map δabc to δefd, then they are congruent. Therefore, Liam is correct.