Question

Find the values of x and y that make these triangles congruent by HL. I need help please

Answer 1

I think the answer is A

Answer 2

A.
`x=5`,
`y=6`

Explanation:

We have been given an image and we are asked to find the values of x and y that will make our given triangles congruent by HL.

Hypotenuse-leg theorem states that if any leg and hypotenuse of one triangle is equal to leg and hypotenuse of another triangle, then both triangles are congruent.

We can see that hypotenuse and one leg of triangle ABC are AC and BC respectively. The hypotenuse and one leg of triangle AED are AD and ED respectively.

To make these our triangles congruent by HL theorem, we can set two equations as:

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

`x=y-1...(2)`

Substituting equation (2) in equation (1) we will get,

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

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

`3y-5=2y+1`

`3y-2y-5+5=2y-2y+5+1`

`y=6`

Therefore, the value of y is 6.

Upon substituting
`y=6` in equation (2) we will get,

`x=6-1`

`x=5`

Therefore, the value of x is 5.

Upon looking at our given choices we can see that option A is the correct choice.