Step 1: Swing Set Repair
A swing set needs repair. The support bar that is at the middle of the A-frame is failing and must
be replaced.
1. 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? Explain.
Answer: Point W is 2.5 feet from point S on the leg. Since legs SI and GI are both
congruent, and since they measure at 5 feet long, the midpoint of each leg would be at 2.5 feet.
Therefore, WS would be 2 and ½ feet.
2. 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.
Answer: A piece of wood that is 36 inches will be long enough to replace the crossbar
labeled WN, but it will need to be cut 6 inches. Triangle SIG is an equilateral triangle, so all the
sides are equal to 5 feet. Since we know WN intersects legs SI and GI at their midpoints, and we
know that half of 5 feet is 2.5 feet, or 30 inches, WN measures at 30 inches across. The
midsegment is half the length of the side to which it's parallel through the application of the
distance formula Therefore, the 36-inch piece of wood will be long enough, but will need to be
cut.
3. Assuming the ground is flat, is WN parallel to the ground?
Answer: Assuming the ground is flat, yes, WN is parallel to the ground. The ground and WN
will never intersect.
Step 2: Using the Centroid
This study source was downloaded by 100000857952895 from CourseHero.com on 01-09-2023 01:09:53 GMT -06:00
https://www.coursehero.com/file/174387426/0205-More-Triangle-Proofs-Collabdocx/
A swing set needs repair. The support bar that is at the middle of the A-frame is failing and must
be replaced.
1. 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? Explain.
Answer: Point W is 2.5 feet from point S on the leg. Since legs SI and GI are both
congruent, and since they measure at 5 feet long, the midpoint of each leg would be at 2.5 feet.
Therefore, WS would be 2 and ½ feet.
2. 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.
Answer: A piece of wood that is 36 inches will be long enough to replace the crossbar
labeled WN, but it will need to be cut 6 inches. Triangle SIG is an equilateral triangle, so all the
sides are equal to 5 feet. Since we know WN intersects legs SI and GI at their midpoints, and we
know that half of 5 feet is 2.5 feet, or 30 inches, WN measures at 30 inches across. The
midsegment is half the length of the side to which it's parallel through the application of the
distance formula Therefore, the 36-inch piece of wood will be long enough, but will need to be
cut.
3. Assuming the ground is flat, is WN parallel to the ground?
Answer: Assuming the ground is flat, yes, WN is parallel to the ground. The ground and WN
will never intersect.
Step 2: Using the Centroid
This study source was downloaded by 100000857952895 from CourseHero.com on 01-09-2023 01:09:53 GMT -06:00
https://www.coursehero.com/file/174387426/0205-More-Triangle-Proofs-Collabdocx/
