Question

which two triangles are congruent? complete the congruence statement.

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Explanation:

Step1: Identify corresponding parts

In congruent triangles, corresponding angles and sides are equal. Looking at the markings (angle - side - angle or side - angle - side congruence indicators).
For \(\triangle VUW\) and \(\triangle CDE\):

• The single - marked angles (\(\angle V\) in \(\triangle VUW\) and \(\angle C\) in \(\triangle CDE\)) are equal.
• The double - marked sides (in \(\triangle VUW\) and \(\triangle CDE\)) are equal.
• The double - marked angles (\(\angle W\) in \(\triangle VUW\) and \(\angle E\) in \(\triangle CDE\)) are equal.

Step2: Write the congruence statement

By the Angle - Side - Angle (ASA) or Side - Angle - Side (SAS) congruence criteria (depending on the order of side and angles, but since all corresponding parts match), we match the vertices.
The vertices of the first triangle \(\triangle VUW\) correspond to the vertices of the second triangle \(\triangle CDE\) as \(V\) to \(C\), \(U\) to \(D\), \(W\) to \(E\)

Answer:

\(\triangle VUW\cong\triangle CDE\)