AnswersVolchWCA 3230 Geometry 3rd Nine Weeks 2025-2026Right Triangle Similarity

Pythagorean Inequalities Answers

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1
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Determine if the segment lengths form a triangle. If so, would the triangle be acute, right, or obtuse?

Question illustration
A
No, the segments do not form a triangle.
B
Yes, the segments would form an acute triangle.
C
Yes, the segments would form a right triangle.
D
Yes, the segments would form an obtuse triangle.
2
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Is the triangle with the given dimensions a right triangle? If so, which angle is the right angle?

Question illustration
A
Yes, is the right angle.
B
Yes, is the right angle.
C
Yes, is the right angle.
D
No, it is not a right triangle.
3

The sides of a triangle have lengths of x, x + 4, and 20. If the longest side is 20, which of the following values of x would make the triangle obtuse?

A
8
B
10
C
12
D
14
4

Analyze the diagram below and answer the question that follows. Analyze the diagram below and answer the question that follows. What is the largest integer value of MO for which rhombus MNOP will have an obtuse angle at P?

Question illustration
A
12
B
14
C
17
D
19
5

Analyze the diagram below and complete the statement that follows. A. C. = D. cannot be determined Please select the best answer from the choices provided

Question illustration
A
A
B
B
C
C
D
D
6

Analyze the diagram below and complete the instructions that follow.Is a right triangle? Why or why not?

Question illustration
A
No, is not a right triangle, because AC would have to be .
B
No, is not a right triangle, because AC would have to be .
C
No, is not a right triangle, because AC would have to be 296.
D
Yes, is a right triangle by the Pythagorean theorem.
8

Can a triangle have an angle that measures ? If so, what type of triangle would it be?

Question illustration
A
Yes, such a triangle would be isosceles.
B
Yes, such a triangle would be obtuse.
C
Yes, such a triangle would be obtuse and isosceles.
D
No such triangle exists.
9

Find an integer, x, such that 2, 4, and x represent the lengths of the sides of an obtuse triangle.

A
2
B
3
C
4
D
6
10

You walk east 720 feet to get from your house to class. After class, you walk southwest 1,044 feet to meet your friends for lunch. When walking the 756 feet back home from lunch, what direction are you traveling?

A
N
B
NE
C
NW
D
W
14

Determine if the values 3, 5, and 7 represent the side lengths of a right triangle, an obtuse triangle, or an acute triangle. Justify your answer.

Answer:

Responses may vary but should include some or all of the following information: Since 3 + 5 > 7, the side lengths can form a valid triangle. Comparing the sum of the squares of the shorter side lengths to the square of the longest side length, we get that 3^2 + 5^2 = 34 and 7^2 = 49. Since 34 < 49, the triangle is obtuse by the obtuse triangle inequality theorem.

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Pythagorean Inequalities Answers — VolchWCA 3230…