Question

Categorize each list of triples into Right Angled Triangles or Not Right Angled Triangles (hint: apply the pythagorean theorem to see if a2+b2=c2 . If it does, then it's a right triangle) (1 point) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Right Angled Triangles Not Right Angled Triangles

Answer 1

To categorize the lists of triples into Right Angled Triangles and Not Right Angled Triangles, we can apply the Pythagorean theorem which states that for a triangle with sides \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the triangle is a right-angled triangle if \(a^2 + b^2 = c^2\).

Please provide the specific lists of triples you want to categorize, and I can help you determine whether they form right-angled triangles or not.

Answer 2

7, 24, 25.
4, 9, 13.
8, 15, 17.
30, 45, 60.

Answer 3

Let's apply the Pythagorean theorem to each list of triples:

1. 7, 24, 25:

   • \(7^2 + 24^2 = 49 + 576 = 625\)
   • \(25^2 = 625\)
   • Since \(7^2 + 24^2 = 25^2\), this is a Right Angled Triangle.

2. 4, 9, 13:

   • \(4^2 + 9^2 = 16 + 81 = 97\)
   • \(13^2 = 169\)
   • Since \(4^2 + 9^2 \neq 13^2\), this is Not a Right Angled Triangle.

3. 8, 15, 17:

   • \(8^2 + 15^2 = 64 + 225 = 289\)
   • \(17^2 = 289\)
   • Since \(8^2 + 15^2 = 17^2\), this is a Right Angled Triangle.

4. 30, 45, 60:

   • \(30^2 + 45^2 = 900 + 2025 = 2925\)
   • \(60^2 = 3600\)
   • Since \(30^2 + 45^2 \neq 60^2\), this is Not a Right Angled Triangle.

Summary:

• Right Angled Triangles: 7, 24, 25; 8, 15, 17
• Not Right Angled Triangles: 4, 9, 13; 30, 45, 60