Triangle Types Quiz: Obtuse Triangle Properties

Questions and Answers

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

2, 2, 3 (correct)

3, 5, 6 (correct)

Which value from the list below, when substituted for x, would represent an acute triangle with side lengths x, x + 4, and 20?

Ella's conclusion that the triangle with side lengths of 10, 11, and 15 is acute is correct.

False

The edge measurements for the sail are listed as 7 ft × 15 ft × 17 ft. The general shape of the sail is a(n) __________ triangle.

obtuse Signup and view all the answers

How does Janice's estimate for the longest side of a right triangle compare to the actual length?

It is under by approximately 0.6 units. Signup and view all the answers

Which are possible lengths of the shortest straw for Marlena's obtuse triangle? Check all that apply.

6 inches Signup and view all the answers

What length must the longest side be for Ramon's triangle to be acute?

C Signup and view all the answers

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. Signup and view all the answers

How would you explain to your classmate how to use side lengths to determine the type of triangle?

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. Signup and view all the answers

Study Notes

Triangle Types and Their Conditions

Sets of numbers representing obtuse triangles include combinations like 2, 2, 3 and 3, 5, 6.
An acute triangle can be formed with sides x, x + 4, and the longest side 20, where x must equal 14.

Evaluating Triangles

Ella analyzed a triangle with sides of 10, 11, and 15, concluding it was acute. However, her procedure is incorrect; the triangle is not acute based on the inequality test.
The measurements of a sail (7 ft, 15 ft, 17 ft) indicate an obtuse triangle configuration.

Length Comparisons

Janice's estimation for the longest side of a right triangle is 25 units, which is approximately 0.6 units low.
Marlena's straws indicate possible lengths for the shortest straw in an obtuse triangle could be 5, 6, or 7 inches.

Creating Acute Triangles

For Ramon to create an acute triangle with sides of 7 inches and 3 inches, the length of the longest side must be appropriately less than the sum of the other two sides.

Path and Triangle Formation

Lin’s walking journey forms an obtuse triangle, with his direction from the gym back home being southwest.

Triangle Classification Explanation

To determine triangle type using side lengths, identify the longest side and check the relationship between the squares of the sides:
- Right triangle: ( a^2 + b^2 = c^2 )
- Acute triangle: ( a^2 + b^2 > c^2 )
- Obtuse triangle: ( a^2 + b^2 < c^2 )
Label the longest side as n, and other sides as a and b for clarity during calculations.

Description

Test your knowledge on the types of triangles and the conditions required for their formation. This quiz will challenge your understanding of acute, obtuse, and right triangles with practical examples and calculations. Are you ready to evaluate triangle properties accurately?

Triangle Types and Properties Quiz