Question

select the correct answer from each drop - down menu.the pair of triangles that are congruent by the asa criterion isthe pair of triangles that are congruent by the sas criterion is

Explanation:

Step1: Recall ASA and SAS criteria

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

Step2: Analyze each pair

• For triangle \(LMN\) and \(XYZ\):
• In \(\triangle LMN\) and \(\triangle XYZ\), we have two angles and the included side.
• Let's assume the angles and side: If we consider the marked angles and the side of length \(5\) (included side between the two marked angles in each triangle).
• For triangle \(ABC\) and \(STU\) (by checking sides and included angles):
• In \(\triangle ABC\) (\(AB = 5\), \(AC=6\), angle between them) and \(\triangle STU\) (\(ST = 5\), \(SU = 6\), angle between them).

Answer:

The pair of triangles that are congruent by the ASA criterion is triangle \(LMN\) and triangle \(XYZ\).
The pair of triangles that are congruent by the SAS criterion is triangle \(ABC\) and triangle \(STU\).