Question

problem 3 identifying parallelograms
vehicle lifts a truck sits on the platform of a vehicle lift. two moving arms raise the
platform until a mechanic can fit underneath. why will the truck always remain
parallel to the ground as it is lifted? explain.
the angles of pqrs change as platform qr rises, but its side lengths remain the same.
both pairs of sides are congruent, so pqrs is a parallelogram by theorem 6 - 8.
by the definition of a parallelogram, ||. since the base of the lift ps lies along the
ground, platform qr, and therefore the truck, will always be to the ground.
got it? 3. reasoning what is the maximum height that the vehicle lift can elevate the
truck? explain.

Explanation:

Step1: Analyze the structure of the lift

The lift forms a parallelogram \(PQRS\). In a parallelogram, opposite sides are equal and parallel. Here, \(PQ = SR\) and \(QR=PS\).

Step2: Consider the properties of a parallelogram

Since \(PQRS\) is a parallelogram, \(QR\parallel PS\). The base \(PS\) lies along the ground.

Step3: Relate the height to the length of the arm

The moving arms (let's assume the length of the non - base sides, say \(PQ\) or \(SR\)) determine the maximum height. If we consider the non - base sides of the parallelogram (assuming they are the vertical - lift - capable arms), and using the Pythagorean theorem (if we consider a right - triangle formed when the lift is at maximum height, with the non - base side of the parallelogram as the hypotenuse). But if we assume the non - base sides of the parallelogram (the arms) are of length \(l = 6\) ft (from the given side lengths in the diagram, assuming the non - base side length is \(6\) ft). When the arm is vertical (the maximum height situation), the maximum height \(h\) that the platform (and thus the truck) can be lifted is equal to the length of the non - base side of the parallelogram.

Answer:

The maximum height that the vehicle lift can elevate the truck is \(6\) ft. This is because when the lift is at its maximum height, the non - base side (the arm) of the parallelogram - shaped lift is perpendicular to the base (the ground - level part of the lift). In a parallelogram, the non - base sides (the arms) have a fixed length, and when oriented vertically, this length gives the maximum vertical displacement (height) of the platform (and the truck on it).