The diagonals of rectangle ABCD are AC and BD. Hallie found that the distances from the point where the diagonals intersects to each vertex were the same. Which of the following conjectures could she make?

a. Diagonals of a rectangle are congruent.
b. Diagonals of a rectangle create equilateral triangles.
c. Diagonals of a rectangle intersect at more than one point.
d. Diagonals of a rectangle are congruent to the width.

Thanks!

If they have the same length (which they do) they are congruent. They do not have to have the same direction. b is true for a square only. c and d are never true.

Find the perimeter of rectangle PQRS with vertices P(0,0), Q(0,7), R(12,7) & S (12,0).

Select one:
a. 38 units
b. 26 units
c. 33 units
d. 45 units

a. Diagonals of a rectangle are congruent.

The diagonals of rectangle ABCD are AC and BD. Hallie found that the distances from the point where the diagonals intersects to each vertex were the same. Which of the following conjectures could she make?

To determine which conjecture Hallie can make, let's examine the given information about the rectangle.

The diagonals of a rectangle are segments that connect opposite vertices. In this case, the diagonals are AC and BD.

Hallie found that the distances from the point where the diagonals intersect to each vertex were the same. This means that the distances from the point of intersection to A, B, C, and D are all equal.

Now let's analyze the given conjectures:

a. Diagonals of a rectangle are congruent.
This conjecture states that the diagonals of a rectangle are equal in length. However, Hallie's observation does not provide enough information to determine if the diagonals are congruent. Therefore, we cannot conclude this conjecture based on the given information.

b. Diagonals of a rectangle create equilateral triangles.
This conjecture suggests that when the diagonals of a rectangle intersect, they create equilateral triangles. However, Hallie's observation does not provide any information about the angles formed by the diagonals. So we cannot conclude this conjecture based on the given information either.

c. Diagonals of a rectangle intersect at more than one point.
This conjecture states that the diagonals of a rectangle intersect at more than one point. However, Hallie's observation indicates that the diagonals intersect at a single point. Thus, we can conclude that this conjecture is not correct.

d. Diagonals of a rectangle are congruent to the width.
This conjecture suggests that the diagonals of a rectangle have the same length as its width. Hallie's observation does not provide enough information to confirm or refute this conjecture. We cannot conclude this conjecture based on the given information.

From the given information, the only conjecture we can conclude is that the distances from the point where the diagonals intersect to each vertex are equal. Therefore, the answer would be:

e. None of the above.

Hope this helps! Let me know if you have any further questions.