Construction of quadrilateral PQRS

Given:
QR = 4.5 cm
RP = SP = 6 cm
RS = 5 cm
QS = 7 cm

Steps:

1. Draw a line segment QR of length 4.5 cm using a ruler.
2. Take a compass and set its width to 6 cm. Place the compass on point Q and draw an arc that intersects QR.
3. Without changing the width of the compass, place it on point R and draw another arc that intersects the previous arc. Label the point of intersection as P.
4. Place the compass on point P and draw an arc with a radius of 6 cm. This arc should intersect the line segment QR.
5. Without changing the width of the compass, place it on point Q and draw an arc that intersects the previous arc. Label the point of intersection as S.
6. Connect points R and S with a straight line segment.
7. Measure the length of RS using a ruler. It should measure 5 cm.
8. Measure the length of QS using a ruler. It should measure 7 cm.
9. Verify that RP and SP both measure 6 cm using a ruler.

Construction of quadrilateral PQRS is complete.

Explanation:
To construct the quadrilateral PQRS, we need to follow the given specifications. Using a ruler and a compass, we can draw the required sides and angles to form the quadrilateral.

First, we draw a line segment QR of length 4.5 cm. Then, we use a compass to draw arcs of radius 6 cm from points Q and R. The arcs intersect at point P.

Next, we draw an arc of radius 6 cm from point P, intersecting QR. This arc intersects the previously drawn arc at point S. Connecting points R and S with a straight line segment forms one of the sides of the quadrilateral.

Finally, we measure the lengths of the sides RS and QS using a ruler. They should measure 5 cm and 7 cm, respectively. We also verify that RP and SP both measure 6 cm, as specified.

By following these steps, we can construct the quadrilateral PQRS that satisfies the given specifications.

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