Question

triangle abc is shown on the coordinate plane.
triangle abc is reflected over the x - axis and then translated vertically to create triangle def.
which statements must be true?
select the two correct statements.
a ∠f ≅ ∠e
b ∠e ≅ ∠b
c ∠d ≅ ∠c
d m∠c = m∠e
e m∠b = m∠c
f m∠a = m∠d

Explanation:

Step1: Understand the transformation

Reflection over the \(x -\)axis and translation are rigid transformations. Rigid transformations (reflections, translations) preserve the shape and size of the figure. So, \(\triangle ABC\cong\triangle DEF\).

Step2: Use the property of congruent triangles

If \(\triangle ABC\cong\triangle DEF\), then corresponding angles are congruent. That is \(\angle A\cong\angle D\), \(\angle B\cong\angle E\), and \(\angle C\cong\angle F\). Congruent angles have equal measures, so \(m\angle A = m\angle D\), \(m\angle B=m\angle E\), \(m\angle C = m\angle F\)

Answer:

B. \(\angle E\cong\angle B\); F. \(m\angle A = m\angle D\)