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

Leg CB = x and leg DE = y - 1. Becuase of the markings on the triangles, we know that CB = DE; therefore, x = y - 1. So let's use that x value when we set the 2 hypotenuses equal to each other. Before any substition, 3x - 2 = 2y + 1. Subbing in for x we have 3(y - 1) - 2 = 2y + 1. And 3y - 3 - 2 = 2y + 1. Combining like terms we have y = 6. If y = 6, we will sub it into the leg equation to find x. x = y - 1; therefore, x = 6 - 1 and x = 5. There you go! x = 5 and y = 6

anjithaka anjithaka · Answer 2 · 2022-06-17T08:09:24+02:00

The values of x and y that make these triangles congruent by HL are

x = 2 and y = 2.

Congruent triangles

For HL, the hypotenuse of one triangle must be congruent to the hypotenuse of the other, and the leg of one triangle must be congruent to the corresponding leg of the other triangle.

This means that we know x = y, and that 2x+3 = 3y+1.

Substituting x in place of y gives us

2x+3 = 3x+1

Subtract 2x from each side:

2x+3-2x = 3x+1-2x

3 = x+1

Subtract 1 from each side:

3-1 = x+1-1

2 = x

This means that x = 2 and y = 2 since they are equal.

To learn more about congruent triangles

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