Respuesta :

rishabhh

We have been given two right triangles. We are asked to find the value of x, which will make both triangles similar by Hypotenuse-Leg congruence.

Hypotenuse-Leg theorem states if one leg and hypotenuse of a right triangle is congruent to the one leg and hypotenuse of other right triangle, then both triangles are congruent.

So we can set an equation as:

2x + 1= 9

Upon subtracting 1 from both sides we will get,

2x+1 -1 = 9-1

2x=8

Dividing both sides of our equation by 2 we will get,

x= 4

akposevictor

For the triangles to be congruent by the HL Congruence Theorem, the value of x must be: C. 4.

What is the HL Congruence Theorem?

If a leg and the hypotenuse of one right triangle are congruent to a corresponding leg and the hypotenuse of another right triangles, the HL Congruence Theorem states that the triangles are congruent to each other.

Therefore, the two corresponding parts of the right triangles are given as:

  • 2x + 1
  • 9

Thus:

2x + 1 = 9 (HL Congruence Theorem)

  • Solve for x

2x = 9 - 1

2x = 8

x = 4

Therefore, for the triangles to be congruent by the HL Congruence Theorem, the value of x must be: C. 4.

Learn more about the HL Congruence Theorem on:

https://brainly.com/question/4155972