For this activity we were asked to explain different shortcuts we could use to prove two triangles congruent, and to find which shortcuts were cheapest to use. To do this, I began by looking at all the different congruence shortcuts. I found 3 possible shortcuts using SAS theorem, one for each angle. I also found 3 shortcuts that used ASA theorem, one for each side. Next I discovered the 6 possible shortcuts that used ASA, and the 1 shortcut that used SSS. Last I found the 2 possible shortcuts that used HL theorem, one for each leg of the triangle. In all I identified 15 usable shortcuts. After finding all the shortcuts I could use, and recording them in the chart. I calculated the cost of measuring each component of the shortcuts by multiplying*…show more content…*

To use this shortcut, you need to measure the 100 yard side, which costs $2,500, the 60° angle, which costs $4,500, and the 200 yard side, which costs $5,000. The total cost of this shortcut is $12,000, which is exactly at the budget. The second shortcut also uses SAS theorem. To use this shortcut you need to measure the 173 yard side, which costs $4,325, the 30° angle, which costs $2,250, and the 200 yard side, which costs $5,000. That means this shortcut’s total cost is $11,575. The next shortcut uses ASA theorem, and it requires you to measure the 30° angle, which costs $2,250, the 200 yard side, which costs $5,000, and the 60° angle, which costs $4,500, for a total cost of $11,750. Another within budget shortcut uses the AAS theorem. This shortcut requires you to find the measures of the 30° angle, the 90° angle, and the 100 yard side, which costs $2,500, $6,750, and $2,500 respectively. That means this shortcut has a total cost of $11,500. The next shortcut also uses AAS. To use it you need to measure the 30° angle, which costs $2,250, the 60° angle, which costs $4,500, 173 yard side, which costs $4,325. In total this shortcut costs $11,075. Another shortcut uses SSS theorem, and it requires for you to measure every side. The 173 yard side costs $4,325, the 100 yard side costs $2,250, and the 200 yard side costs $5,000, making the total cost

To use this shortcut, you need to measure the 100 yard side, which costs $2,500, the 60° angle, which costs $4,500, and the 200 yard side, which costs $5,000. The total cost of this shortcut is $12,000, which is exactly at the budget. The second shortcut also uses SAS theorem. To use this shortcut you need to measure the 173 yard side, which costs $4,325, the 30° angle, which costs $2,250, and the 200 yard side, which costs $5,000. That means this shortcut’s total cost is $11,575. The next shortcut uses ASA theorem, and it requires you to measure the 30° angle, which costs $2,250, the 200 yard side, which costs $5,000, and the 60° angle, which costs $4,500, for a total cost of $11,750. Another within budget shortcut uses the AAS theorem. This shortcut requires you to find the measures of the 30° angle, the 90° angle, and the 100 yard side, which costs $2,500, $6,750, and $2,500 respectively. That means this shortcut has a total cost of $11,500. The next shortcut also uses AAS. To use it you need to measure the 30° angle, which costs $2,250, the 60° angle, which costs $4,500, 173 yard side, which costs $4,325. In total this shortcut costs $11,075. Another shortcut uses SSS theorem, and it requires for you to measure every side. The 173 yard side costs $4,325, the 100 yard side costs $2,250, and the 200 yard side costs $5,000, making the total cost

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