Question

1. in the diagram of \\( \triangle a b c \\) and \\( \triangle d e f \\) below, \\( \overline{a b} \cong \overline{d e}, \angle a \cong \angle d \\), and \\( \angle b \cong \angle e \\).

which method can be used to prove \\( \triangle a b c \cong \triangle d e f \\)?
(1) sss (2) sas (3) asa (4) hl

Explanation:

Step1: Recall triangle congruence criteria

• SSS (Side - Side - Side): All three sides of one triangle are equal to the corresponding sides of another triangle.
• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle.
• HL (Hypotenuse - Leg): Applicable for right - angled triangles.

Step2: Analyze the given information

We are given that \(\overline{AB}\cong\overline{DE}\), \(\angle A\cong\angle D\), and \(\angle B\cong\angle E\). Here, the side \(\overline{AB}\) is between \(\angle A\) and \(\angle B\) in \(\triangle ABC\), and the side \(\overline{DE}\) is between \(\angle D\) and \(\angle E\) in \(\triangle DEF\).

Answer:

(3) ASA