Question

Which statement correctly describes the relationship between Δjkl and Δj′k′l′?

1) Δjkl is congruent to Δj′k′l′ because you can map Δjkl to Δj′k′l′ using a rotation of 90° counterclockwise about the origin, which is a rigid motion.
2) Δjkl is congruent to Δj′k′l′ because you can map Δjkl to Δj′k′l′ using a translation 5 units up, which is a rigid motion.
3) Δjkl is not congruent to Δj′k′l′ because there is no sequence of rigid motions that maps Δjkl to Δj′k′l′.
4) Δjkl is congruent to Δj′k′l′ because you can map Δjkl to Δj′k′l′ using a reflection across the x-axis, which is a rigid motion.

Answer 1

The correct statement that describes the relationship between Δjkl and Δj′k′l′ is option 4) Δjkl is congruent to Δj′k′l′ because you can map Δjkl to Δj′k′l′ using a reflection across the x-axis, which is a rigid motion.

Step-by-step explanation:

The correct statement that describes the relationship between Δjkl and Δj′k′l′ is option 4) Δjkl is congruent to Δj′k′l′ because you can map Δjkl to Δj′k′l′ using a reflection across the x-axis, which is a rigid motion.

When you reflect Δjkl across the x-axis, it will result in Δj′k′l′, and the two triangles will have the same size and shape. Therefore, they are congruent.

Option 1 is incorrect because a rotation of 90° counterclockwise about the origin does not result in congruent triangles. Option 2 is incorrect because a translation 5 units up does not preserve the size and shape of the triangles. Option 3 is incorrect because there is a sequence of rigid motions (reflection across the x-axis) that maps Δjkl to Δj′k′l′.