Changes of angles, geometry homework help

Part B: Using Geometry (30 points)Be sure to show all your work for full credit.
A commuter airline company, Geometry Central, currently serves four cities; Addison, Braxton,
Clayton, and Davidson – labeled A, B, C, and D respectively. Geometry Central has hired you to
build their new hub in a more centrally located area where service between all four cities will be
reduced. You have determined the location of the new hub to be point H. In addition, the hub will add
4 new routes to the schedule: AH, BH, CH, and DH.
D
30°
45°
А
200 mi
B
1. How could you apply the Triangle Inequality Theorem to write an inequality involving AX,CX and
AC; assuming X is not the same point as He? How could you rewrite the inequality to include AH and
CH instead of AC? (2 points)
2. The executives at Geometry Central want to know why your location at point H (AH + BH + CH +
DH) is the smallest combined distance between the cities. Give an indirect proof or argument in
favor to explain why the airline should build the new hub at the intersection of the diagonals AC and
BD. (Hint: Assume a different point X results in a smaller combined distance. Then show how AX +
CX compares to AH + CH.) (5 points)
3. How can you find AC? What is the relationship between AB and BC? Round your answer to the
nearest tenth. (4 points)
4. How are DB and DC related? What are their measures? Round your answer to the nearest
tenth. (4 points)
5. Presently, travelers who want to fly from Addison to Clayton must fly through Braxton. After the
new hub is built, travelers will have a shorter route from Addison to the new hub and then to Clayton.
How many miles will this save? Round your answer to the nearest tenth. (2 points)
6. Presently, travelers who want to fly from Braxton to Davidson must fly through Clayton. After the
new hub is built, travelers will have a shorter route from Braxton to the new hub and then to
Davidson. How many miles will this save? Round your answer to the nearest tenth. (2 points)
7. Only comparing the sides of quadrilateral ABCD, which route appears to be the longest? How
could you show that this route is longer than AD ? (2 points)
8. After the new airport hub is built, Geometry Central will serve a meal on its longest non-stop flight.
On which route should they serve the meal? How do you know this is the longest route? Write a
paragraph proof. (5 points)
9. Use A ACD to find the range of possible distances for the route from Addison to Davidson. Must
show your work for full credit. (4 points)