Question

A swing set needs repair. The support bar that is at the middle of the A-frame is failing and must be replaced.

An image of a swing set is shown with triangle SIG drawn with a midpoint W on side SI and midpoint N on side IG.

The legs of the frame SI and GI are each 5 ft long. If the crossbar WN intersects legs SI and GI at their midpoints, how far is point W from point S on the leg? Justify your answer and show all calculations.
The distance between point S and point G is 5 feet. Will a piece of wood that is 36 in long be long enough to replace the crossbar labeled WN? Justify your answer and show all calculations.
Assuming the ground is flat, is WN parallel to the ground? Justify with the applicable theorem.

Answer 1

Answer:

• Yes to both questions

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Given triangle SIG with:

• W is midpoint of SI and N is midpoint of IG,
• SI = GI = 5 ft,
• SG = 5 ft.

According to the given details, WN is midsegment.

We know properties of a midsegment:

• Midsegment is parallel to one side of the triangle,
• Midsegment is half the length of the parallel side.

Therefore:

• WN = SG/2 = 5 ft / 2 = 2.5 ft

We know that:

• 1 foot = 12 inches

Then:

• WN = 2.5 ft = 2.5*12 in = 30 in

Since 36 in > 30 in, it is long enough to replace the crossbar WN.

If ground is flat, WN is parallel to the ground as it is parallel to SG.