Answer:
C) x = 3, y = 2
Step-by-step explanation:
The given diagram shows two right triangles. The shortest leg and hypotenuse of one right triangle is congruent to the shortest leg and hypotenuse of the other right triangle, as indicated by the same number of tick marks on each corresponding line segment.
The Hypotenuse-Leg Triangle Congruence Theorem (HL) states that if the hypotenuse and one leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the two triangles are congruent.
To find the values of x and y that make the two triangles congruent by the HL Theorem, set each pair of corresponding sides equal to each other and form a system of equations:
[tex]\begin{cases}x = y + 1\\x + 3 = 3y\end{cases}[/tex]
Substitute the first equation into the second equation and solve for y:
[tex](y+1)+3=3y\\\\y+4=3y\\\\4=2y\\\\y=2[/tex]
Now, substitute the found value of y into the first equation and solve for x:
[tex]x = 2 + 1\\\\x=3[/tex]
Therefore, the values of x and y that make the given triangles congruent by the HL Theorem are:
[tex]\Large\boxed{\boxed{x = 3,\; y = 2}}[/tex]
