Question

Help me please. Find the values of x and y that make these triangles congruent by the HL Theorum.

Answer 1

According to the HL theorem for right-triangles, one leg and the hypotenuse must be equal, what does that mean?

well it means that 3y = x + 3, and that y + 1 = x, when does that happen anyway?  let's see,

$\bf \begin{cases} 3y=x+3\\ y+1=\boxed{x} \end{cases}\implies 3y=\boxed{y+1}+3\implies 3y=y+4 \\\\\\ 2y=4\implies y=\cfrac{4}{2}\implies y=2\\\\ -------------------------------\\\\ \textit{and since we know that }y+1 =x\implies (2)+1=x\implies 3=x$