Question

Consider that ΔXYZ is reflected across the y-axis and translated 2 units down.

Choose all TRUE statements about the transformation.

X'Y' ≅ XY
∠Z ≅ ∠Z'
ΔXYZ is not congruent to ΔX'Y'Z'.
Reflecting and translating the triangle change its shape and size.

Answer 1

Answer:

X'Y' ≅ XY

∠Z ≅ ∠Z'

Step-by-step explanation:

we know that

A transformation that does not alter the size or shape of a figure is called a Rigid Transformation

Translations, rotations and reflections are rigid transformations

Verify each statement

case 1) X'Y' ≅ XY

The statement is true

Because

Reflecting and translating the triangle not change its shape or its size

The corresponding sides of the image and the pre-image are congruent

case 2) ∠Z ≅ ∠Z'

Because

Reflecting and translating the triangle not change its shape or its size

The corresponding angles of the image and the pre-image are congruent

case 3) ΔXYZ is not congruent to ΔX'Y'Z'

The statement is false

Because

ΔXYZ is congruent to ΔX'Y'Z'

case 4) Reflecting and translating the triangle change its shape and size

The statement is false

Because

Reflecting and translating the triangle not change its shape or its size