Question

1. state what information is needed in order to make the given congruent reason true.

Explanation:

Step1: Analyze ASA congruence rule

ASA requires two pairs of congruent angles and the included congruent side between them.

Step2: Identify given congruent parts

In $\triangle MDE$ and $\triangle FED$, $\angle MDE = \angle FED$, side $DE = ED$ (common side).

Step3: Find missing part for ASA

We need the other pair of angles that include the common side: $\angle MED = \angle EDF$.

Step1: Analyze AAS congruence rule

AAS requires two pairs of congruent angles and one non-included congruent side.

Step2: Identify given congruent parts

In $\triangle TRS$ and $\triangle FDE$, $\angle T = \angle D$, $\angle S = \angle E$.

Step3: Find missing part for AAS

We need a pair of non-included congruent sides: either $TR = FD$, $RS = DE$, or $TS = FE$. The most direct non-included side pair matching the angle order is $TR = FD$.

Answer:

We need $\boldsymbol{\angle MED \cong \angle EDF}$ (or $\boldsymbol{\angle MED = \angle EDF}$) to satisfy the ASA triangle congruence rule.

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