Consider triangles EJH and EIH . overline (HJ)bot overline (JE),overline (HI)bot overline (IE) overline (JE)cong overline (IE) Which criteria for triangle congruence could be used to show that Delta EJHcong Delta EIH Side-Side-Side Side-Side-Angle Hypotenuse-Leg There is not enough information to show the triangles are congruent.

To determine which criteria for triangle congruence could be used to show that \(\triangle EJH \cong \triangle EIH\), we need to analyze the given information and apply it to the properties of the triangles.Given:1. \(\overline{HJ} \perp \overline{JE}\) - This means that \(\overline{HJ}\) is perpendicular to \(\overline{JE}\), so \(\angle HJE\) is a right angle.2. \(\overline{HI} \perp \overline{IE}\) - This means that \(\overline{HI}\) is perpendicular to \(\overline{IE}\), so \(\angle HIE\) is a right angle.3. \(\overline{JE} \cong \overline{IE}\) - This means that the lengths of \(\overline{JE}\) and \(\overline{IE}\) are equal.Step 1: Identify the right angles in the triangles.Both \(\triangle EJH\) and \(\triangle EIH\) have a right angle, which means they are both right triangles.Step 2: Identify congruent sides.We are given that \(\overline{JE} \cong \overline{IE}\), which means that the side opposite the right angle in both triangles is congruent.Step 3: Identify the hypotenuse and legs of the right triangles.In a right triangle, the hypotenuse is the side opposite the right angle, and the legs are the two sides that form the right angle. In this case, \(\overline{JE}\) and \(\overline{IE}\) are the hypotenuses of \(\triangle EJH\) and \(\triangle EIH\) respectively, and \(\overline{HJ}\) and \(\overline{HI}\) are the legs.Step 4: Apply the right triangle congruence criteria.For right triangles, the Hypotenuse-Leg (HL) congruence theorem states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent.In our case, we have:- The hypotenuses \(\overline{JE}\) and \(\overline{IE}\) are congruent.- The legs \(\overline{HJ}\) and \(\overline{HI}\) are both perpendicular to their respective hypotenuses, forming right angles, which means they are congruent by definition of perpendicular lines intersecting at a point (they are both radii of the same circle or segments from the same point E to point H).Therefore, we have two congruent sides (hypotenuse and one leg) and a right angle, which is enough to conclude that the triangles are congruent by the Hypotenuse-Leg (HL) theorem.Answer:The criteria for triangle congruence that could be used to show that \(\triangle EJH \cong \triangle EIH\) is Hypotenuse-Leg (HL).