Question

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

A: x = 3, y = 2

B: x=4, y = 8

C:x= 2, y = 3

D: x = –2, y = 3

Answer 1

B. x=4 y=8

Explanation:

Piece of cake!!!

The hypotenuse leg theorem (hl theorem) tells us that if the two hypotenuses and two legs of right triangles are congruent, then the triangles are congruent.

In these case, if the hypotenuse y-3 is congruent with x+1 and y-5 is congruent with 2x-5 the two triangles are congruent.

So we have a system of equations

(1)

`y-3=x+1\\y=x+4\\`

and

(2)

`2x-5=y-5\\2x=y`

then

We take 2 and replace in 1.

`y=x+4\\(2x)=x+4\\2x-x=4\\x=4`

if x=4, then we replace it in 2.

`2x=y\\2(4)=y\\8=y`

So B is the answer!!!