Question

what additional information is required in order to know that the triangles are congruent by hl theorem?
gi ≅ xv
gh ≅ xw
∠h ≅ ∠v
∠g ≅ ∠x

Explanation:

Step1: Recall the HL (Hypotenuse - Leg) Theorem

The HL Theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent.
In the given right - triangles \(\triangle GHI\) and \(\triangle XWV\), we already know that \(HI = WV\) (the legs are congruent as shown by the tick marks).

Step2: Identify the hypotenuse and leg requirements

For the HL Theorem, we need to show that the hypotenuses of the two right - triangles are congruent.
The hypotenuse of \(\triangle GHI\) is \(GH\), and the hypotenuse of \(\triangle XWV\) is \(XW\).

Answer:

\(GH\cong XW\)