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.
To determine which statement about the two quadrilaterals must be true, we can analyze the given information.
The measure of the side of the rhombus GHIJ is equal to the measure of the side of the square RSTU.
Now, let's evaluate each statement:
A. Their angle measures are equal.
The question does not provide any information about the angle measures of the rhombus and square. Hence, we cannot conclude that their angle measures are equal.
B. Their diagonal measures are equal.
The diagonal measures of a rhombus are not necessarily equal to the diagonal measures of a square, as rhombi have distinct properties. Therefore, we cannot conclude that their diagonal measures are equal.
C. Their areas are equal in measure.
Since we know that the side of the rhombus is equal to the side of the square, and the area of a square is equal to the side squared, we can determine that the area of the square RSTU is equal to the area of the rhombus GHIJ. Therefore, the statement "Their areas are equal in measure" must be true.
D. Their perimeters are equal.
The perimeter of a rhombus is calculated by multiplying the length of one side by four. Similarly, the perimeter of a square is calculated by multiplying the length of one side by four. Since the measure of the side of the rhombus is equal to the measure of the side of the square, we can conclude that their perimeters are equal. Therefore, the statement "Their perimeters are equal" must also be true.
In summary, the statement that must be true about the two quadrilaterals is:
C. Their areas are equal in measure.
D. Their perimeters are equal.