Question

A diagonal connects vertex upper A in the top left to vertex upper C in the bottom right. Another diagonal line connects vertex upper B in the lower left to vertex upper D in the top right. These diagonals intersect at a point upper O, in the middle of the parallelogram.


Because congruent diagonals prove that a parallelogram is a rectangle, what value of x proves that parallelogram ABCD
𝐴
𝐵
𝐶
𝐷
is a rectangle if AC=48
𝐴
𝐶
=
48
and DO=7x+3
𝐷
𝑂
=
7
𝑥
+
3
?

(1 point)
Responses

x=8
𝑥
=
8

x equals 8

x=4
𝑥
=
4

x equals 4

x=6
𝑥
=
6

x equals 6

x=3

Answer 1

Because the diagonals of a rectangle are congruent, BD = AC = 48. The diagonals of a parallelogram bisect each other, so DO = BD/2 = 24. Set 7x + 3 = 24:

7x + 3 = 24
7x = 21
x = 3

Answer: x = 3.