Find the values of x and y that make these triangles congruent by the hl theorem

Option C x=2, y=6

Step-by-step explanation:

we know that

The hypotenuse leg theorem, (HL theorem), 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

so

In this problem

Equate the hypotenuses of both right triangles

x+3=y-1 > x=y-4 > equation A

Equate the legs of both right triangles

y-3=2x-1 > equation B

substitute equation A in equation B and solve for y

y-3=2(y-4)-1

y-3=2y-8-1

2y-y=-3+9

y=6

Find the value of x

x=y-4 > x=6-4=2

therefore

x=2, y=6

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.