Question

triangle fde is a rotation of scalene triangle abc. which statements are correct? select all that are correct. m∠b = m∠c m∠d = m∠c m∠d = m∠b m∠f = m∠b m∠e = m∠c m∠e = m∠d

Explanation:

Step1: Recall rotation property

When a triangle is rotated, corresponding angles are congruent. In \(\triangle ABC\) and \(\triangle FDE\), \(\angle A\) corresponds to \(\angle F\), \(\angle B\) corresponds to \(\angle D\), and \(\angle C\) corresponds to \(\angle E\).

Step2: Analyze each option

• \(m\angle B=m\angle C\): \(\triangle ABC\) is scalene, so \(m\angle B

eq m\angle C\).

• \(m\angle D = m\angle C\): Since \(\angle D\) corresponds to \(\angle B\) and \(\angle C\) corresponds to \(\angle E\), \(m\angle D

eq m\angle C\).

• \(m\angle D=m\angle B\): Correct as they are corresponding angles in the rotation.
• \(m\angle F=m\angle B\): \(\angle F\) corresponds to \(\angle A\), so \(m\angle F

eq m\angle B\).

• \(m\angle E=m\angle C\): Correct as they are corresponding angles in the rotation.
• \(m\angle E = m\angle D\): In general, for a non - isosceles triangle (scalene here), \(m\angle E

eq m\angle D\).

Answer:

\(m\angle D=m\angle B\), \(m\angle E=m\angle C\)