Podcast
Questions and Answers
Which sets of three numbers represent the sides of an obtuse triangle? Check all that apply.
Which sets of three numbers represent the sides of an obtuse triangle? Check all that apply.
Which value from the list below, when substituted for x, would represent an acute triangle with side lengths x, x + 4, and 20?
Which value from the list below, when substituted for x, would represent an acute triangle with side lengths x, x + 4, and 20?
14
Ella's conclusion that the triangle with side lengths of 10, 11, and 15 is acute is correct.
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.
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.
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How does Janice's estimate for the longest side of a right triangle compare to the actual length?
How does Janice's estimate for the longest side of a right triangle compare to the actual length?
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Which are possible lengths of the shortest straw for Marlena's obtuse triangle? Check all that apply.
Which are possible lengths of the shortest straw for Marlena's obtuse triangle? Check all that apply.
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What length must the longest side be for Ramon's triangle to be acute?
What length must the longest side be for Ramon's triangle to be acute?
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What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form?
What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form?
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How would you explain to your classmate how to use side lengths to determine the type of triangle?
How would you explain to your classmate how to use side lengths to determine the type of triangle?
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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.
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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?
