Question

1. state the additional congruency statement(s) needed to prove \\(\delta abc \cong \delta fgh\\) for the given theorem. (1 point)

a. what is the missing side or angle needed to prove \\(\delta abc \cong \delta fgh\\) using the sas theorem?

b. what is the missing side or angle needed to prove \\(\delta abc \cong \delta fgh\\) using the asa theorem?

Explanation:

Identify given congruent parts

Using the Triangle Congruence Postulates knowledge point
From the markings on the triangles \(\Delta ABC\) and \(\Delta FGH\):

• Angle marking: \(\angle A \cong \angle F\)
• Side marking: \(AC \cong FH\)

Determine missing part for SAS

Using the Triangle Congruence Postulates knowledge point

• SAS requires two sides and their included angle.
• The given angle is \(\angle A\) (included between \(AB\) and \(AC\)) and \(\angle F\) (included between \(FG\) and \(FH\)).
• Since \(AC \cong FH\), the other side forming the angle must be congruent: \(AB \cong FG\).

Determine missing part for ASA

Using the Triangle Congruence Postulates knowledge point

• ASA requires two angles and their included side.
• The given side is \(AC\) (included between \(\angle A\) and \(\angle C\)) and \(FH\) (included between \(\angle F\) and \(\angle H\)).
• Since \(\angle A \cong \angle F\), the other adjacent angle must be congruent: \(\angle C \cong \angle H\).

Answer:

Question 8a

\(AB \cong FG\) (or \(AB = FG\))

Question 8b

\(\angle C \cong \angle H\) (or \(\angle C = \angle H\))