The measure of the side of rhombus GHIJ is equal to the measure of the side of square RSTU. Which statement about the two quadrilaterals must be true?
A. Their angle measures are equal.
B. Their diagonal measures are equal.
C. Their areas are equal in measure.
D. Their perimeters are equal.
Visualize a square sort of "squished".
The only thing that would remain constant is the perimeter.
Since the measure of the side of rhombus GHIJ is equal to the measure of the side of square RSTU, we can conclude that their perimeters are equal.
Therefore, the correct answer is D. Their perimeters are equal.
To determine which statement about the two quadrilaterals must be true, we need to analyze the given information.
The first piece of information is that the measure of the side of rhombus GHIJ is equal to the measure of the side of square RSTU. This tells us that the sides of the rhombus and the square have the same length.
Let's consider each statement one by one:
A. "Their angle measures are equal." We cannot make any conclusions about the angle measures based on the information given. The equal length of the sides does not necessarily mean that the angles are equal.
B. "Their diagonal measures are equal." Diagonals are typically different for rhombuses and squares. In a rhombus, the diagonals are not equal, while in a square, they are equal. Therefore, this statement cannot be true.
C. "Their areas are equal in measure." The area of a rhombus is given by the formula A = (d₁ * d₂) / 2, where d₁ and d₂ are the lengths of the diagonals. In a square, where all sides are equal, the area is given by A = s², where s is the length of the side. Since the sides of the rhombus and square are equal in length, their areas would only be equal if the diagonals of the rhombus are equal in measure. However, there is no information given about the diagonals of the rhombus. Therefore, we cannot determine if this statement is true.
D. "Their perimeters are equal." The perimeter is the sum of the lengths of all the sides of a shape. Since the sides of the rhombus and square are equal in length, their perimeters will also be equal. Therefore, we can conclude that the statement "Their perimeters are equal" must be true.
In conclusion, the statement that must be true is D. "Their perimeters are equal."