AnswersRMA FL-1206310-Geometry Semester 2Triangle Classification Theorems

Triangle Classification Theorems Answers

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Which sets of three of numbers represent the sides of an obtuse triangle? Check all that apply.4, 7, 8 3, 4, 52, 2, 36, 8, 93, 5, 6

A
4, 7, 8
B
3, 4, 5
C
2, 2, 3
D
6, 8, 9
E
3, 5, 6
2
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What did you include in your response? Check all that apply.

A
If a2 + b2 = c2, the triangle is right.
B
If c2 < a2 + b2, the triangle is acute.
C
If c2 > a2 + b2, the triangle is obtuse.
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Question text not available

Answer:

obtuse

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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.

A
8
B
10
C
12
D
14
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Which statement best summarizes Ella’s work?

A
Ella’s procedure and conclusion are correct.
B
Ella’s procedure is correct, but her conclusion is incorrect.
C
Ella’s procedure is incorrect, but her conclusion is correct.
D
Ella’s procedure and conclusion are incorrect.
112871

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?

A
It is exactly correct.
B
It is under by approximately 0.6 units.
C
It is over by approximately 0.6 units.
D
It is over by 13 units.
112872

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.

A
5 inches
B
6 inches
C
7 inches
D
8 inches
E
9 inches
112873

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?

A
exactly inches
Option A
B
greater than inches but less than 10 inches
Option B
C
less than inches but greater than 7 inches
Option C
D
not enough information given
Option D
112874

What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form?

A
Lin walked south, creating a right triangle.
B
Lin walked southwest, creating an obtuse triangle.
C
Lin walked southeast, creating an acute triangle.
D
Lin walked directly east, creating a right triangle.
112875

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.

A
8
B
10
C
12
D
14
112876

Which statement best summarizes Ella’s work?

A
Ella’s procedure and conclusion are correct.
B
Ella’s procedure is correct, but her conclusion is incorrect.
C
Ella’s procedure is incorrect, but her conclusion is correct.
D
Ella’s procedure and conclusion are incorrect.
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⇒ obtuse

Answer:

obtuse

112878

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?

A
It is exactly correct.
B
It is under by approximately 0.6 units.
C
It is over by approximately 0.6 units.
D
It is over by 13 units.
112879

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.

A
5 inches
B
6 inches
C
7 inches
D
8 inches
E
9 inches
112880

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?

A
exactly inches
Option A
B
greater than inches but less than 10 inches
Option B
C
less than inches but greater than 7 inches
Option C
D
not enough information given
Option D
112881

What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form?

A
Lin walked south, creating a right triangle.
B
Lin walked southwest, creating an obtuse triangle.
C
Lin walked southeast, creating an acute triangle.
D
Lin walked directly east, creating a right triangle.
112882

Which sets of three of numbers represent the sides of an obtuse triangle? Check all that apply.4, 7, 8 3, 4, 52, 2, 36, 8, 93, 5, 6

A
4, 7, 8
B
3, 4, 5
C
2, 2, 3
D
6, 8, 9
E
3, 5, 6
112883

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

Answer:

To determine the type of triangle, first identify the longest side as c and the other two sides as a and b. Then calculate a² + b² and compare it to c². If c² = a² + b², the triangle is a right triangle. If c² a² + b², the triangle is obtuse.

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