Question

1. what additional information is needed to prove △tux≅△deo by hl? ∠x≅∠o

overline{tx}≅overline{do}
overline{oe}≅overline{ux}
∠u≅∠e

Explanation:

Step1: Recall HL - Hypotenuse - Leg theorem

HL theorem states that if the hypotenuse and one leg of a right - triangle are congruent to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent.

Step2: Identify hypotenuses and legs in given triangles

In right - triangles $\triangle TUX$ and $\triangle DEO$, we already know that one pair of legs are congruent (as shown by the single cross - mark on the legs). We need the hypotenuses to be congruent. The hypotenuse of $\triangle TUX$ is $UX$ and the hypotenuse of $\triangle DEO$ is $OE$. For $\triangle TUX\cong\triangle DEO$ by HL, we need $\overline{OE}\cong\overline{UX}$.

Answer:

$\overline{OE}\cong\overline{UX}$