Question

complete the proof that \\( \triangle uvw - \triangle ust \\).
answer
in order to verify that \\( \triangle uvw - \triangle ust \\) by aa-, the additional information needed is the measure of
by using
submit answer

Explanation:

Step1: Identify vertical angles

$\angle SUV$ and $\angle TUS$ are vertical angles. By the vertical - angles theorem, $\angle SUV=\angle TUS$.

Step2: Apply AA similarity criterion

For two triangles $\triangle UVW$ and $\triangle UST$, if we can show that two pairs of corresponding angles are equal, then the triangles are similar by the AA (angle - angle) similarity criterion. We already have one pair of equal angles ($\angle SUV=\angle TUS$ from vertical angles). We need to show that another pair of angles is equal. From the figure, we can see that $\angle W=\angle T$ (the marked angles).

Answer:

In order to verify that $\triangle UVW\sim\triangle UST$ by AA, the additional information needed is that $\angle W = \angle T$ by using the vertical - angles theorem for $\angle SUV=\angle TUS$.