Question

4
a
v
r
g
y
δvar ≅ δ____ by ____

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. So, \(\angle ARV=\angle GRY\)

Step2: Use given side - angle information

We are given that \(VR = GR\) (marked in the figure). Also, \(\angle V=\angle G\) (given in the figure).
By the Angle - Side - Angle (ASA) congruence criterion:
In \(\triangle VAR\) and \(\triangle YGR\), \(\angle V=\angle G\), \(VR = GR\), \(\angle ARV=\angle YRG\)

Answer:

\(\triangle YGR\) by \(ASA\)