Question

1. what additional information would need to be given to prove the triangles congruent by sas?

∠lga ≅ ∠dga
∠gal ≅ ∠gad
the triangles cannot be proven congruent by sas.
∠gla ≅ ∠gda

Explanation:

Step1: Recall the SAS (Side - Angle - Side) congruence criterion

For two triangles \(\triangle DGA\) and \(\triangle LGA\), we already know that \(DG = LG\) (given by the marks on the sides) and \(GA=GA\) (common side).

Step2: Analyze each option

• Option \(\angle GLA\cong\angle GDA\): This is not the included angle between the known sides for the SAS criterion.
• Option \(\angle GAL\cong\angle GAD\): This is not the included angle between the known sides for the SAS criterion.
• Option \(\angle LGA\cong\angle DGA\): This is the included angle between \(LG\) and \(GA\) in \(\triangle LGA\) and between \(DG\) and \(GA\) in \(\triangle DGA\). If \(\angle LGA\cong\angle DGA\), then by the SAS (Side - Angle - Side) congruence criterion (\(LG = DG\), \(\angle LGA=\angle DGA\), \(GA = GA\)), \(\triangle DGA\cong\triangle LGA\)

Answer:

\(\angle LGA\cong\angle DGA\)