Question

Find the values of x and y that make these triangles congruent by the HL Theorem.

https://dlap.gradpoint.com/Resz/~0.CnMRm0iSgmA-gRAB.gO6Ir5JEZSeDvUe-CcqgYGFBp0lKI9Sn136AoTqXAsI/7234256,888/Assets/questions/quiz/geometry/geoconrt/geoconrt-f-15.png

x = 3, y = 2

x = 4, y = 8

x = –2, y = 3

x = 2, y = 3

Answer 1

do you have any idea of what the HL theorem is?

Answer 2

and do you know what makes two triangles congruent?

Answer 3

Basically, the hypotenuse leg theorem says that: If the hypotenuse and one leg of a triangle are congruent (same) to the hypotenuse and leg of another triangle then these two triangles are congruent.
So, to solve this problem set the hypotenuse of each triangle equal to one another and that'll be eqn. 1. Then set the leg of each triangle to one another and you'll get eqn. 2. We set them equal to each other because we need them to be the same (congruent). From this you can use substitution/elimination to solve and find x and y.