Question

state what additional information is required in order to know that the triangles are congruent for the reason given.

1. sas
2. aas
3. asa
4. sss

Explanation:

Step1: Recall SAS congruence criterion

SAS (Side - Angle - Side) requires two sides and the included angle of one triangle to be congruent to two sides and the included angle of another triangle. For the given triangles with some sides marked congruent, we need the included angle. So for $\triangle EFG$ and $\triangle BCA$, we need $\angle E\cong\angle B$.

Step2: Recall AAS congruence criterion

AAS (Angle - Angle - Side) requires two angles and a non - included side of one triangle to be congruent to two angles and the corresponding non - included side of another triangle. For $\triangle LMN$ and $\triangle BCD$, we have one side and one angle marked. We need $\angle N\cong\angle C$.

Step3: Recall ASA congruence criterion

ASA (Angle - Side - Angle) requires two angles and the included side of one triangle to be congruent to two angles and the included side of another triangle. For $\triangle JHT$ and $\triangle SUT$, we have one side and one angle marked. We need $\angle J\cong\angle S$.

Step4: Recall SSS congruence criterion

SSS (Side - Side - Side) requires all three sides of one triangle to be congruent to all three sides of another triangle. For $\triangle FQS$ and $\triangle RQS$, we have two sides marked. We need $FQ\cong RQ$.

Answer:

1. $\angle E\cong\angle B$
2. $\angle N\cong\angle C$
3. $\angle J\cong\angle S$
4. $FQ\cong RQ$