Question

What additional info is needed to prove Δ TUX congruent to Δ DEO by HL?

Answer 1

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

Answer: 1.Line seg, TX is ≈ to Line Seg, DO. 

Answer 2

Answer:

1. $\text{Line segment TX}\cong\text{ Line segment DO}$

Step-by-step explanation:

We have been given two right triangles and we are asked to choose the correct option that is needed to prove Δ TUX congruent to Δ DEO by HL.

Since HL (Hypotenuse-Leg) congruence 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 triangles are congruent.

We can see that in triangle TUX, UX is hypotenuse and in triangle DEO, EO is hypotenuse.

We have been given that hypotenuse of both triangle are equal, so to prove these triangles congruent by HL congruence either side length TU should be equal to side length DE or length of side TX should be equal to side DO.  

Upon looking at our given choices we can see that only 1st option is correct.

$\text{Line segment TX}\cong\text{ Line segment DO}$

Therefore, 1st option is the correct choice.