Question

1. what additional information is needed to prove the triangles are congruent for the reason given. you can notate it on the diagram or write it in words.

a. asa
b. sas
c. aas

Explanation:

Step1: Recall ASA (Angle - Side - Angle)

ASA requires two angles and the included side. For $\triangle KLM$ and $\triangle STU$, we know $\angle K=\angle S$ and $\angle L=\angle T$, so we need $KL = ST$.

Step2: Recall SAS (Side - Angle - Side)

SAS requires two sides and the included angle. For $\triangle EFG$ and $\triangle LMN$, we know $EF = LM$ and $\angle E=\angle M$, so we need $EG=LN$.

Step3: Recall AAS (Angle - Angle - Side)

AAS requires two angles and a non - included side. For $\triangle PQR$ and $\triangle JKL$, we know $\angle Q=\angle K$ and $PQ = JK$, so we need $\angle R=\angle L$.

Answer:

a. $KL = ST$
b. $EG=LN$
c. $\angle R=\angle L$