Question

1. state the additional congruency statement(s) needed to prove ( \triangle abccong\triangle fgh ) for the given theorem.

(1 point)
a. what is the missing side or angle needed to prove ( \triangle abccong\triangle fgh ) using the sas theorem?
b. what is the missing side or angle needed to prove ( \triangle abccong\triangle fgh ) using the asa theorem?

Explanation:

Step1: Recall SAS and ASA congruence rules

• SAS (Side - Angle - Side): Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.
• ASA (Angle - Side - Angle): Two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

Step2: Analyze for SAS (for part a)

We know that \(\angle A=\angle F\) (given as angles at \(A\) and \(F\) are marked equal) and \(AC = FH\) (given as the sides \(AC\) and \(FH\) are marked equal). For SAS, we need the sides adjacent to the given angle to be in proportion. So, we need \(AB=FG\)

Step3: Analyze for ASA (for part b)

We know that \(\angle A=\angle F\) (given as angles at \(A\) and \(F\) are marked equal) and \(AC = FH\) (given as the sides \(AC\) and \(FH\) are marked equal). For ASA, we need \(\angle C=\angle H\)

Answer:

a. \(AB = FG\)
b. \(\angle C=\angle H\)