Question

as = at
which of the following triangles would be congruent in statement 3 in the proof?
ars and ats
ars and aqt
art and aqs

Explanation:

Step1: Recall ASA (Angle - Side - Angle) congruence criterion

ASA states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Analyze the given information

We know \(AR = AQ\) (given), \(\angle1=\angle3\) (given), and \(\angle R=\angle Q\) (from the property of isosceles triangle \(AR = AQ\)).
For \(\triangle ARS\) and \(\triangle AQT\):

• \(AR = AQ\) (given)
• \(\angle1=\angle3\) (given)
• \(\angle R=\angle Q\) (from step 1)

The included side for \(\triangle ARS\) is \(AR\) with angles \(\angle1\) and \(\angle R\), and for \(\triangle AQT\) is \(AQ\) with angles \(\angle3\) and \(\angle Q\)

Answer:

ARS and AQT