Question

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

x = -3 y - 4
x = -4 y-3
x = -6. y-5
x = -5, y = 6

Answer 1

`x=5, y=6`

Explanation:

we know that

If triangles ABC and AED are congruent, then its corresponding sides are congruent

so

BC=ED

AC=AD

substitute the given values

`x=y-1` ----> equation A

`3x-2=2y+1` ----> equation B

solve the system by substitution

substitute equation A in equation B

`3(y-1)-2=2y+1`

solve for y

`3y-3-2=2y+1`

`3y-2y=1+5`

`y=6`

Find the value of x

`x=y-1` ---->
`x=6-1=5`

therefore

`x=5, y=6`