Question

which two triangles are congruent? complete the congruence statement.

Explanation:

Step1: Identify corresponding angles and sides

In triangle \(VUT\), \(UT\) has a mark. In triangle \(E CD\), \(EC\) has two marks. In triangle \(JHI\), \(JH\) has two marks. Also, looking at the angles, in \(\triangle VUT\), \(\angle T\) is a large - marked angle and \(\angle U\) is a small - marked angle. In \(\triangle JHI\), \(\angle H\) is a large - marked angle and \(\angle J\) is a small - marked angle.

Step2: Use the Angle - Angle - Side (AAS) congruence criterion

The AAS (Angle - Angle - Side) congruence criterion states that if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, then the two triangles are congruent.
For \(\triangle VUT\) and \(\triangle JHI\):

• \(\angle T=\angle H\) (the large - marked angles)
• \(\angle U=\angle J\) (the small - marked angles)
• \(UT = JH\) (the sides with one mark)

Answer:

\(\triangle VUT\cong\triangle JHI\)