According to HL theorem if one leg and hypotenuse of one right triangle are equal to one leg and hypotenuse of other right triangle, then the triangles are congruent.

By using this theorem we can set up the system of equations as follows:

x=y+1 ...(1)

2x+3= 3y + 3 ..(2)

By using equation (1) next step is to plug in y+1 for x in equation (2). So,

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

2y + 2 + 3 = 3y + 3 By using distribution property.

2y + 5 = 3y + 3

2y + 5 - 5 = 3y + 3 - 5 Subtract 5 from each side.

2y = 3y - 2

2y - 3y = -2 Subtract 3y from each sides.

-y = -2

So, y=2

Next step is to plug in y=2 in equation (1) to get the value of x. Hence,

x= 2+1

So, x=3 and y=2 make these triangles congruent.

So, the correct choice is 3. x = 3, y = 2.

7 0

3 years ago

Cody bagged the plastic bottles after a recycling drive. He placed 15 bottles in the first bag, 90 bottles in the second bag, 36

stepan [7]

Answer: repeating sequence

Step-by-step explanation:

3 0

3 years ago

Choose the equation of the line parallel to the x axis

Aleonysh [2.5K]

Answer:

D just imagine a straight flat line going through y=4

4 0

3 years ago

Zoey made 6 3/4 cups of fruit salad for a picnic. At the picnic, they ate 1/3 of the fruit salad. How much of the fruit salad di

Aleks04 [339]

Answer:

9/4 cups

Step-by-step explanation:

6 3/4 = 27/4

27/4 * 1/3 = 27/12

27/12 = 9/4

4 0

3 years ago