Question

1. given: \\( \angle d \cong \angle t, \angle e \cong \angle u, \overline{eo} \cong \overline{ux} \\) write a congruence statement for the pair of triangles shown. \\( \triangle tux \cong \triangle deo \\) \\( \triangle tux \cong \triangle edo \\) \\( \triangle tux \cong \triangle doe \\) \\( \triangle tux \cong \triangle oed \\)

Explanation:

Step1: Match the corresponding angles

Given \( \angle D=\angle T\), \( \angle E = \angle U\). In congruent triangles, the order of the letters in the congruence statement should match the corresponding angles.

Step2: Match the corresponding sides

Given \( \overline{EO}\cong\overline{UX}\). So, the first triangle has vertices \(T\), \(U\), \(X\) and the second triangle has vertices \(D\), \(E\), \(O\) (since \( \angle T\) corresponds to \( \angle D\), \( \angle U\) corresponds to \( \angle E\) and \( \angle X\) corresponds to \( \angle O\) (by the fact that the sum of angles in a triangle is \(180^{\circ}\), if two angles of one triangle are equal to two angles of another triangle, the third angles are also equal)).

Answer:

\(\triangle TUX\cong\triangle DEO\)