the diagonal of rectangle abcd measures 2 inches in length. what is the length of line segment ab? 1 inch √3…

Explanation:

Step1: Recall 30 - 60 - 90 triangle rule

In a right - triangle (e.g., $\triangle ABD$ in rectangle $ABCD$), if the angles are $30^{\circ}$, $60^{\circ}$, and $90^{\circ}$, and the hypotenuse $BD = 2$ inches. The side opposite the $30^{\circ}$ angle is half of the hypotenuse, and the side opposite the $60^{\circ}$ angle is $\sqrt{3}$ times the side opposite the $30^{\circ}$ angle.

Step2: Identify the position of side AB

In right - triangle $\triangle ABD$, $\angle ADB=30^{\circ}$, $\angle BAD = 90^{\circ}$, and $\angle ABD=60^{\circ}$. The side $AB$ is opposite the $30^{\circ}$ angle.

Step3: Calculate the length of AB

According to the 30 - 60 - 90 triangle ratio, if the hypotenuse $BD = c = 2$ inches, and the side opposite the $30^{\circ}$ angle is $a$, then $a=\frac{c}{2}$. So $AB = 1$ inch.

Answer:

1 inch