### Identifying Right Triangles **Tell whether each triangle is a right triangle.** #### Example 13 **Diagram Details:** - The triangle is labeled with three sides: 18, 24, and 30 units. - Side lengths are clearly marked along the edges of the triangle. **Question:** - Is this triangle a right triangle? **Answer Choices:** 1. Yes, the triangle is a right triangle. 2. No, the triangle is NOT a right triangle. **Explanation:** To determine if this triangle is a right triangle, use the Pythagorean Theorem. For a triangle with sides \(a\), \(b\), and hypotenuse \(c\), the relationship \(a^2 + b^2 = c^2\) must hold true. Here, let's check: \[18^2 + 24^2 = 30^2\] Calculations: \[18^2 = 324\] \[24^2 = 576\] \[30^2 = 900\] Adding the squares of the two shorter sides: \[324 + 576 = 900\] Since \(900 = 900\), the Pythagorean Theorem holds true, and therefore the triangle with sides 18, 24, and 30 is indeed a right triangle.
### Identifying Right Triangles **Tell whether each triangle is a right triangle.** #### Example 13 **Diagram Details:** - The triangle is labeled with three sides: 18, 24, and 30 units. - Side lengths are clearly marked along the edges of the triangle. **Question:** - Is this triangle a right triangle? **Answer Choices:** 1. Yes, the triangle is a right triangle. 2. No, the triangle is NOT a right triangle. **Explanation:** To determine if this triangle is a right triangle, use the Pythagorean Theorem. For a triangle with sides \(a\), \(b\), and hypotenuse \(c\), the relationship \(a^2 + b^2 = c^2\) must hold true. Here, let's check: \[18^2 + 24^2 = 30^2\] Calculations: \[18^2 = 324\] \[24^2 = 576\] \[30^2 = 900\] Adding the squares of the two shorter sides: \[324 + 576 = 900\] Since \(900 = 900\), the Pythagorean Theorem holds true, and therefore the triangle with sides 18, 24, and 30 is indeed a right triangle.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![### Identifying Right Triangles
**Tell whether each triangle is a right triangle.**
#### Example 13
**Diagram Details:**
- The triangle is labeled with three sides: 18, 24, and 30 units.
- Side lengths are clearly marked along the edges of the triangle.
**Question:**
- Is this triangle a right triangle?
**Answer Choices:**
1. Yes, the triangle is a right triangle.
2. No, the triangle is NOT a right triangle.
**Explanation:**
To determine if this triangle is a right triangle, use the Pythagorean Theorem. For a triangle with sides \(a\), \(b\), and hypotenuse \(c\), the relationship \(a^2 + b^2 = c^2\) must hold true.
Here, let's check:
\[18^2 + 24^2 = 30^2\]
Calculations:
\[18^2 = 324\]
\[24^2 = 576\]
\[30^2 = 900\]
Adding the squares of the two shorter sides:
\[324 + 576 = 900\]
Since \(900 = 900\), the Pythagorean Theorem holds true, and therefore the triangle with sides 18, 24, and 30 is indeed a right triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa53c426-a760-4829-b362-653d3877b060%2Fc73e7803-185e-4e13-a39e-32f49e31c455%2Fgtkgi4f.jpeg&w=3840&q=75)
Transcribed Image Text:### Identifying Right Triangles
**Tell whether each triangle is a right triangle.**
#### Example 13
**Diagram Details:**
- The triangle is labeled with three sides: 18, 24, and 30 units.
- Side lengths are clearly marked along the edges of the triangle.
**Question:**
- Is this triangle a right triangle?
**Answer Choices:**
1. Yes, the triangle is a right triangle.
2. No, the triangle is NOT a right triangle.
**Explanation:**
To determine if this triangle is a right triangle, use the Pythagorean Theorem. For a triangle with sides \(a\), \(b\), and hypotenuse \(c\), the relationship \(a^2 + b^2 = c^2\) must hold true.
Here, let's check:
\[18^2 + 24^2 = 30^2\]
Calculations:
\[18^2 = 324\]
\[24^2 = 576\]
\[30^2 = 900\]
Adding the squares of the two shorter sides:
\[324 + 576 = 900\]
Since \(900 = 900\), the Pythagorean Theorem holds true, and therefore the triangle with sides 18, 24, and 30 is indeed a right triangle.
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