Triangle Classification Theorems Assignment and Quiz

A right triangle has side lengths 4 units, 5 units, and x units. It is unknown if the missing length is the longest or shortest side. Rounded to the nearest tenth, what is the difference between the possible values of x?

3.4 units

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

10, 24, 26

The sides of a triangle have length x, x + 4, and 20. If the length of the longest side is 20, which value of x would make the triangle acute?

14

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

2, 2, 3 3, 5, 6

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

Which set of numbers can represent the side lengths, in inches, of an acute triangle?

5, 7, 8

The longest side of an acute isosceles triangle is 8 centimeters. Rounded to the nearest tenth, what is the smallest possible length of one of the two congruent sides?

5.7 cm

An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?

6 < s < 12.8

The shorter sides of an acute triangle are x cm and 2x cm. The longest side of the triangle is 15 cm. What is the smallest possible whole-number value of x?

7

Two sides of an obtuse triangle measure 12 inches and 14 inches. The longest side measures 14 inches. What is the greatest possible whole-number length of the unknown side?

7 inches

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown. What is the smallest possible perimeter of the triangle, rounded to the nearest hundredth?

72.44 in.

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.

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

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.

Arielle is building the wooden framework for the roof of a house. She needs the angle created by the vertical and horizontal boards of the frame to be a right angle. The height of the vertical board is 12 feet. The length of the horizontal board is 15 feet. The support beam that will connect the ends of the two boards measures 20 feet. Which is true regarding the triangular frame?

It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.

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.

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?

less than √58 inches but greater than 7 inches

On the packaging for a triangular sail, the edge measurements for the sail are listed as 7 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

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

obtuse, because 6^2 + 10^2 < 12^2