I need help with this problem please, and please make it legible.

Prove that a parallelogram is a rectangle if and only if its diagonals are equal in length. (This fact is often D exploited by carpenters.) A (0,0) B . . . . . In the given diagram, A is located at the origin. Notice that AC and BD are the two vectors representing the diagonals of the rectangle. What must be true if the diagonals are equal? O A. AC . BD = 1 O B. AC + BD = 1 O C. AC = BD O D. AC . BD = 0What is another way of writing AC? O A. AB + CD O B. AD + BC O C. AC + DB O D. AB + BC What is another way of writing BD? O A. BA + CD O B. BC + AD O C. BD + AC O D. BA + ADWhich of the following is a true statement? O A. AD = BC O B. AB = AD O C. AC = BD O D. BC = BD Given the equality in the previous step, what is yet another way of writing BD? O A. AB + AD OB. AC - BC O C. - AD - BD O D. - AB + BC> > Recall the equation found in the very rst step. where it was noticed that AC and BD are the two vectors representing the diagonals of the rectangle. Square both sides of that equation to create a new equation. Which of the following is equal to that new equation? 0A. |;5|2=1_2|5|+|55|2 o 3- IRE|2+IEE|2+2(KE-EE) earnerarea oc. (EAg 2:55.532 on. (x5.;5+5.5)2=o Which of the following must be true, based on the equation found in the previous step? > > CA. AC-BD=0 OB. KE-KE=0 0c. EE-Ew on. XE-5=o Which of the following is true of two vectors whose dot product is 0? O A. They are parallel. O B. They bisect each other. 0 C. They are equal in magnitude. O D. They are orthogonal. Which of the following properties is generally true of rectangles but not generally true of parallelograms, meaning that any parallelogram with this property is a rectangle? O A. Opposite sides of a rectangle are parallel. O B. The interior angles of a rectangle are right angles. 0 C. The sides of a rectangle are all equal. 0 D. Opposite sides of a rectangle are equal