Question 1
Measurements of each object:
- Stick 1: 5 inches
- Stick 2: 7 inches
- Stick 3: 10 inches
Application of Triangle Inequality Theorem:
According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, the sum of Stick 1 and Stick 2 is 12 inches, which is greater than the length of Stick 3 (10 inches). Therefore, these three objects can form a triangle.
Question 2
Triangle type: Obtuse triangle
Angle measures: 60 degrees, 100 degrees, 20 degrees
Triangle Angle Sum Theorem calculation: 60 + 100 + 20 = 180 degrees
Drawings of possible triangles:
- Side lengths don't matter for this question
Question 3
Units used: Miles
Fill out the table with the distance between each point on the Bermuda Triangle:
- Miami, FL to Bermuda: 1032 miles
- Bermuda to San Juan, Puerto Rico: 1099 miles
- San Juan, Puerto Rico to Miami, FL: 1045 miles
Apply the Triangle Inequality Theorem:
The sum of the distances between any two points must be greater than the distance between the third point in order for the Bermuda Triangle to be a true triangle. In this case, 1032 + 1099 = 2131 miles, which is greater than the distance from San Juan, Puerto Rico to Miami, FL (1045 miles). Therefore, the Bermuda Triangle is not a true triangle according to the Triangle Inequality Theorem.
There are no results for Investigate the construction of a triangle in these portfolio activities. Use what you have learned about the Triangle Angle Sum Theorem and the Triangle Inequality Theorem to create your submissions. Record your answers below. Question 1 Find three objects (sticks, utensils, yarn, toys, books, etc.) that could represent the sides of a triangle. Can you make a triangle with these three objects? Use the Triangle Inequality Theorem explain why or why not. Measurements of each object: Application of Triangle Inequality Theorem: Question 2 Decide if you want to make an acute, obtuse, or right triangle. Select three angle measures. How is the Triangle Angle Sum Theorem important for creating triangles? How many triangles can you make with three angle measures? Using your ruler and protractor, draw one or more (if possible) examples. Triangle type: Angle measures: Triangle Angle Sum Theorem calculation: Drawings of possible triangles: Question 3 Is the Bermuda Triangle really a triangle? The Bermuda Triangle features vertices in Miami, Florida; Bermuda; and San Juan, Puerto Rico. Find the distances between these points and remember to keep all measures in the same units. Using what you have learned about triangles, determine if the Bermuda Triangle is really a triangle. Units used: Fill out the table with the distance between each point on the Bermuda Triangle. Points Distance Miami, FL to Bermuda Bermuda to San Juan, Puerto Rico San Juan, Puerto Rico to Miami, FL Apply the Triangle Inequality Theorem: Is the Bermuda Triangle really a triangle? Explain.
3 answers
Is the Bermuda Triangle really a triangle? Explain.
Based on the distances between the three points of the Bermuda Triangle (Miami, FL; Bermuda; and San Juan, Puerto Rico), it does not meet the criteria of a triangle according to the Triangle Inequality Theorem. The sum of the distances between any two points must be greater than the distance between the third point in order for it to be a true triangle. In this case, the sum of the distances between Miami, FL and Bermuda (1032 miles) and Bermuda and San Juan, Puerto Rico (1099 miles) is 2131 miles, which is less than the distance between San Juan, Puerto Rico and Miami, FL (1045 miles). Therefore, the Bermuda Triangle is not a true triangle and does not meet the requirements to be considered a geometric triangle.
3 answers