Question

1. (02 03 lc)

if ( \triangle abccong\triangle fde ), which of the following statements is true? (1 point)
( angle acongangle f )
( angle bcongangle f )
( angle acongangle d )
( angle bcongangle e )

Explanation:

Step1: Recall the property of congruent triangles

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

Step2: Check each option

• For the option \(\angle A\cong\angle F\): Since \(\triangle ABC\cong\triangle FDE\), by the property of congruent triangles (corresponding parts of congruent triangles are congruent - CPCTC), \(\angle A\) and \(\angle F\) are corresponding angles.
• For the option \(\angle B\cong\angle F\): \(\angle B\) corresponds to \(\angle D\) (not \(\angle F\)) as per the congruence \(\triangle ABC\cong\triangle FDE\).
• For the option \(\angle A\cong\angle D\): \(\angle A\) corresponds to \(\angle F\) (not \(\angle D\)) as per the congruence \(\triangle ABC\cong\triangle FDE\).
• For the option \(\angle B\cong\angle E\): \(\angle B\) corresponds to \(\angle D\) (not \(\angle E\)) as per the congruence \(\triangle ABC\cong\triangle FDE\).

Answer:

\(\angle A\cong\angle F\) (the first option)