Question

from each drop - down menu.
the pair of triangles that are congruent by the asa criterion is
the pair of triangles that are congruent by the sas criterion is
triangle bac and triangle uts
triangle bac and triangle rqp
triangle pqr and triangle stu
triangle bac and triangle xyz

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 triangle \(BAC\) and \(UTS\)

For triangle \(BAC\) and \(UTS\):

• In \(\triangle BAC\), \(AB = 5\), \(AC=6\), \(\angle A\) (included angle between \(AB\) and \(AC\))
• In \(\triangle UTS\), \(UT = 5\), \(US = 6\), \(\angle U\) (included angle between \(UT\) and \(US\))

We check the angles and sides. By ASA criterion, we can see that \(\triangle BAC\cong\triangle UTS\)

Step3: Analyze triangle \(BAC\) and \(XYZ\)

For triangle \(BAC\) and \(XYZ\):

• In \(\triangle BAC\), \(AB = 5\), \(AC = 6\), \(\angle A\)
• In \(\triangle XYZ\), \(XY=5\), \(XZ = 6\), \(\angle X\)

By SAS criterion, \(\triangle BAC\cong\triangle XYZ\)

Answer:

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