The figure below shows a rectangle abcd having diagonals ac and db:

anastasia wrote the following proof to show that diagonals of rectangle abcd are congruent:

C is the correct statement " In ΔADC and ΔBCD AD=BC, opposite sides of  a rectangle are congruent"which completes the proof .

Step-by-step explanation:

Given: A figure shows a rectangle ABCD having diagonals AC and DB.

Anastasia wrote the  proof  given in picture to show that diagonals of rectangle ABCD are congruent.

We can see the Statement 2 which tells that AB=CD, opposite sides of  a rectangle are congruent. In Statement 3 she used Pythagoras theorem to show AC²= BD² by using Statement 1 and 2.

Thus we can see she need to introduce two triangles named as ACD and BCD and the remaining sides to write the proof is AD=BC with correct reason i.e. opposite sides of  a rectangle are congruent.

Therefore Statement 1 would be In ΔADC and ΔBCD AD=BC, opposite sides of  a rectangle are congruent.

It appears that each x value is multiplied by 4 to get the y value.