Question

Question
Which statement correctly describes the relationship between △JKL and △J′K′L′?

Responses

△JKL is not congruent to △J′K′L′ because there is no sequence of rigid motions that maps △JKL to △J′K′L′.
triangle J K L is not congruent to triangle J prime K prime L prime because there is no sequence of rigid motions that maps triangle J K L to triangle J prime K prime L prime .

△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a rotation of 90° counterclockwise about the origin, which is a rigid motion.
triangle J K L is congruent to triangle J prime K prime L prime because you can map triangle J K L to triangle J prime K prime L prime using a rotation of 90° counterclockwise about the origin, which is a rigid motion.

△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a translation 5 units up, which is a rigid motion.
triangle J K L is congruent to triangle J prime K prime L prime because you can map triangle J K L to triangle J prime K prime L prime using a translation 5 units up, which is a rigid motion.

△JKL is congruent to △J′K′L′ because you can map △JKL to △J′K′L′ using a reflection across the x-axis, which is a rigid motion.
triangle J K L is congruent to triangle J prime K prime L prime because you can map triangle J K L to triangle J prime K prime L prime using a reflection across the x -axis, which is a rigid motion.
An x y coordinate plane is shown. In quadrant 1 triangle J K L has vertices at begin ordered pair 2 comma 1 end ordered pair, begin ordered pair 5 comma 1 end ordered pair and begin ordered pair 5 comma 5 end ordered pair, respectively. In quadrant 4 triangle J prime K prime L prime has vertices at begin ordered pair 2 comma negative 1 end ordered pair, begin ordered pair 5 comma negative 1 end ordered pair and begin ordered pair 5 comma negative 4 end ordered pair, respectively.

Answer 1

△JKL is not congruent to △J′K′L′ because there is no sequence of rigid motions that maps one to the other.

Reason: their side lengths differ.
- For △JKL: JK = 3, KL = 4, JL = 5 (a 3-4-5 right triangle).
- For △J′K′L′: J′K′ = 3, K′L′ = 3, J′L′ = 3√2 (an isosceles triangle).

Because the corresponding side lengths are not the same, the triangles are not congruent.