Question

question
determine the relationship between the two triangles and whether or not they can be proven
to be congruent.

answer attempt 2 out of 2
the two triangles are related by
side-side-side (sss)
side-angle-side (sas)
angle-side-angle (asa)
angle-angle-side (aas)
hypotenuse-leg (hl)
side-side-angle (ssa)
angle-angle-angle (aaa)
, so the triangles

Explanation:

Step1: Identify Triangle Type

The triangle shown is a right triangle with two legs marked as equal (isosceles right triangle). For right triangles, the Hypotenuse - Leg (HL) congruence criterion applies when we have a right angle, hypotenuse, and a leg. But also, since it's a right triangle with two legs equal, another way: if we consider two right triangles with hypotenuse and one leg equal, HL is used. Wait, but the triangle here has two legs marked (so legs are equal) and a right angle. If we are comparing two such triangles, the HL (Hypotenuse - Leg) or also, since it's a right triangle, and if we have hypotenuse and leg, but also, in the case of isosceles right triangles, HL can be applied. Wait, the key is that for right triangles, HL is a congruence criterion. Let's recall: HL 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. Also, in the given triangle, it's a right triangle with two legs marked (so legs are congruent). So if we have two right triangles, each with hypotenuse and one leg (or two legs) congruent, HL is applicable. So the relationship is Hypotenuse - Leg (HL) for right triangles. Also, note that SSA is not a valid congruence criterion in general, but HL is a special case of SSA for right triangles. But among the options, HL is a valid congruence criterion for right triangles. So the two triangles (assuming the other triangle is also a right triangle with hypotenuse and leg congruent to this one) are related by Hypotenuse - Leg (HL), so they can be proven congruent.

Step2: Select the Criterion

From the dropdown, the correct criterion for right triangles (when comparing hypotenuse and leg) is Hypotenuse - Leg (HL). So we select HL as the relationship.

Answer:

Hypotenuse - Leg (HL)