A quadrilateral has vertices $$ A(4,5), B(2,4), C(4,3) $$, and $$ D(6,4) $$. Which statement about the quadrilateral is true A. $$ A B C D $$ is a parallelogram with noncongruent adjacent sides. B. $$ A B C D $$ is a trapezoid with only one pair of parallel sides. C. $$ A B C D $$ is a rectangle with noncongruent adjacent sides. D. $$ A B C D $$ is a square. E. $$ A B C D $$ is a rhombus with non-perpendicular adjacent sides.

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1. Label the vertices:
   - $$ A(4,5) $$
   - $$ B(2,4) $$
   - $$ C(4,3) $$
   - $$ D(6,4) $$

2. Compute the side lengths using the distance formula.

- For side $$ AB $$:
     $$
     AB = \sqrt{(2-4)^2 + (4-5)^2} = \sqrt{(-2)^2 + (-1)^2} = \sqrt{4+1} = \sqrt{5}
     $$
     
   - For side $$ BC $$:
     $$
     BC = \sqrt{(4-2)^2 + (3-4)^2} = \sqrt{2^2 + (-1)^2} = \sqrt{4+1} = \sqrt{5}
     $$
     
   - For side $$ CD $$:
     $$
     CD = \sqrt{(6-4)^2 + (4-3)^2} = \sqrt{2^2 + 1^2} = \sqrt{4+1} = \sqrt{5}
     $$
     
   - For side $$ DA $$:
     $$
     DA = \sqrt{(4-6)^2 + (5-4)^2} = \sqrt{(-2)^2 + 1^2} = \sqrt{4+1} = \sqrt{5}
     $$
     
   Since all four sides are equal, the quadrilateral is a rhombus.

3. Check whether it is a square (i.e., has a right angle):

- Compute the slopes of adjacent sides.
   
     For $$ AB $$:
     $$
     \text{slope of } AB = \frac{4-5}{2-4} = \frac{-1}{-2} = \frac{1}{2}
     $$
     
     For $$ AD $$:
     $$
     \text{slope of } AD = \frac{4-5}{6-4} = \frac{-1}{2} = -\frac{1}{2}
     $$
     
   - Since the slopes of $$ AB $$ and $$ AD $$ are not negative reciprocals (the negative reciprocal of $$\frac{1}{2}$$ is $$-2$$, not $$-\frac{1}{2}$$), the adjacent sides are not perpendicular. Thus, the quadrilateral is not a square.

4. Identify the correct statement:
   
   The quadrilateral $$ ABCD $$ is a rhombus with non-perpendicular adjacent sides.

The true statement is option E.
The quadrilateral $$ ABCD $$ is a rhombus with non-perpendicular adjacent sides.

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