Question

quadrilaterals are formed on the side of a fishing tackle box by the adjustable shelves and connecting pieces. explain why the shelves are always parallel to each other no matter what their position is.
in order to explain why the shelves are always parallel to each other no matter what their position is, start by identifying any given information. select all that apply.
□ a. (overline{ad}congoverline{bc}) □ b. (overline{ac}perpoverline{bd})
□ c. (bc = 2cdot ab) □ d. (overline{ab}paralleloverline{cd})
□ e. abcd is a parallelogram. □ f. (overline{ab}congoverline{cd})
□ g. (overline{ad}paralleloverline{bc}) □ h. (overline{ac}) bisects (overline{bd})

Explanation:

Step1: Analyze the properties of a parallelogram

In a parallelogram, opposite sides are congruent and parallel.

Step2: Check the given options

• Option A: $\overline{AD}\cong\overline{BC}$ (opposite sides of a parallelogram are congruent).
• Option D: $\overline{AB}\parallel\overline{CD}$ (opposite sides of a parallelogram are parallel).
• Option E: ABCD is a parallelogram (given by the markings of congruent sides which is a property of a parallelogram).
• Option F: $\overline{AB}\cong\overline{CD}$ (opposite sides of a parallelogram are congruent).
• Option G: $\overline{AD}\parallel\overline{BC}$ (opposite sides of a parallelogram are parallel).

Options B ($\overline{AC}\perp\overline{BD}$ - there is no indication of perpendicular diagonals), C ($BC = 2\cdot AB$ - no such length relation given), and H ($\overline{AC}$ bisects $\overline{BD}$ - not relevant to proving parallel shelves) are incorrect.

Answer:

A. $\overline{AD}\cong\overline{BC}$, D. $\overline{AB}\parallel\overline{CD}$, E. ABCD is a parallelogram, F. $\overline{AB}\cong\overline{CD}$, G. $\overline{AD}\parallel\overline{BC}$