Triangle Classification Theorems Assignment

Which sets of three of numbers represent the sides of an obtuse triangle? Check all that apply.

2, 2, 3 3, 5, 6

Which value from the list below, when substituted for x, would represent an acute triangle with side lengths x, x+ 4, and 20? Assume that the longest side of the triangle is of length 20 units.

14

Marlena has 3 straws. Two straws have the lengths shown. She does not know the length of the shortest straw, but when she forms a triangle with all three, the triangle is obtuse. Which are possible lengths of the shortest straw? Check all that apply.

5 inches 6 inches 7 inches

Your classmate is unsure about how to use side lengths to determine the type of triangle. How would you explain this to your classmate?

BOTH OF THESE ARE CORRECT! :) Sample answer: First, look at the side lengths a, b, and c, where c is the longest. Then take the sum of a squared and b squared and compare it to c squared. If they are equal, the triangle is a right triangle. If c squared is less than a squared plus b squared, the triangle is acute. If c squared is greater than a squared plus b squared, the triangle is obtuse. My response: Label the sides of the triangle (the longest side and hypotenuse being n and the other sides being a and b). Square all of the sides. Now take side a and side b and add them. If it is less than the hypotenuse it is an obtuse triangle, if the sides together are more than the hypotenuse then the triangle is an acute one, and if the sides and hypotenuse are equal to each other it is a right triangle.

Ramon wants to make an acute triangle with three pieces of wood. So far, he has cut wood lengths of 7 inches and 3 inches. He still needs to cut the longest side. What length must the longest side be in order for the triangle to be acute?

C

Ella's geometry teacher asked each student to devise a problem and write out its solution. Here is Ella's work: A triangle has side lengths of 10, 11, and 15. What type of triangle is it? Procedure: 102 ?? 112 + 152 100 ?? 121 + 225 100 < 346 Conclusion: This triangle is an acute triangle. Which statement best summarizes Ella's work?

Ella's procedure and conclusion are incorrect.

Janice examines the given triangle and estimates that the longest side has a length of 25 units―if it is a right triangle. How does her estimate compare to the actual length?

It is under by approximately 0.6 units.

To get from his house to the lecture hall at school, Lin walked west 651 feet. After class, he walked northeast 910 feet to the gym. Finally, he walked 615 feet back to his house from the gym. What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form?

Lin walked southwest, creating an obtuse triangle.

On the packaging for a triangular sail, the edge measurements for the sail are listed as7 ft × 15 ft × 17 ft. Without unfurling the sail, you want to determine if the sail forms a right triangle, an acute triangle, or an obtuse triangle. Using the tools from this lesson, you determine that the general shape of the sail is a(n) ___________ triangle.

obtuse