Question

use the following picture to classify the following statements as true or false.
drag & drop the answer
\\( \overline { a c } \cong \overline { d f } \\)
\\( \triangle a b c \cong \triangle d e f \\) by asa
\\( \triangle a b c \cong \triangle d e f \\) by aas
\\( \angle a b c \cong \angle f d e \\)
\\( \angle b a c \cong \angle e d f \\)
\\( \overline { b c } \cong \overline { e f } \\)
true
false

Explanation:

Step1: Check triangle congruence criteria

ASA (Angle - Side - Angle) and AAS (Angle - Angle - Side) are criteria for triangle congruence. For \(\triangle ABC\) and \(\triangle DEF\), if \(\angle BAC\cong\angle EDF\), \(\angle ABC\cong\angle DEF\), and \(BC\cong EF\), then \(\triangle ABC\cong\triangle DEF\) by AAS.

Step2: Check angle and side congruence

\(\angle ABC\) is not congruent to \(\angle FDE\). Also, \(AC\) is not congruent to \(DF\). And \(\triangle ABC\) is not congruent to \(\triangle DEF\) by ASA.

Answer:

True: \(\angle BAC\cong\angle EDF\), \(\triangle ABC\cong\triangle DEF\) by AAS, \(BC\cong EF\)
False: \(\angle ABC\cong\angle FDE\), \(AC\cong DF\), \(\triangle ABC\cong\triangle DEF\) by ASA