Discover the Properties of Triangle ABC: Vertices, Lengths, and Angles

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In summary, the conversation discusses the vertices of a triangle, which are A=(1,-1,-6), B=(4,4,2) and C=(-2,2,-4). The participants are trying to determine whether the triangle is a right triangle. They use the Pythagorean theorem (a^2 + b^2 = c^2) to find the lengths of the sides, and then use that information to determine if the triangle has a right angle at A. They also discuss different scenarios and equations (||AB||^2 + ||BC||^2 = ||AC||^2, ||AB||^2 + ||BC||^2 - ||CA||^2 = 152, ||AB||^
  • #1
shiri
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A=(1,-1,-6), B=(4,4,2) and C=(-2,2,-4) are the vertices of a triangle.

a) ||AB||^2 + ||BC||^2 = ||AC||^2
b) ||AB||^2 + ||BC||^2 - ||CA||^2 = 152
c) ||AB||^2 + ||BC||^2 + ||CA||^2 = 196
d) The triangle has a right angle at A
e) The triangle is a right triangle


a) T
b) F, should be sqrt152
c) F, should be sqrt196
d) Not sure
e) Not sure

Can somebody help me out here, please? I'll be very appreciated
 
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  • #2
For a, b, and c, all your answers are wrong. What are you getting for |AB|^2, |BC|^2, and |AC|^2?

For d, if you know the lengths of each side of a triangle, how can you tell if a particular angle is a right angle?
For e, if you know the lengths of each side of a triangle, how can you tell whether any angle is a right angle?
 

1. What is a triangle?

A triangle is a polygon with three sides and three vertices. It is one of the basic shapes in geometry and is often used in various mathematical and scientific applications.

2. How do you name a triangle?

A triangle is typically named by using the capital letters of its three vertices, in alphabetical order. For example, triangle ABC would have vertices at points A, B, and C.

3. What are the properties of a triangle?

The properties of a triangle include its three angles, which always add up to 180 degrees, and its three sides, which can vary in length. The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

4. How do you find the length of a side in a triangle?

The length of a side in a triangle can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In non-right triangles, the length of a side can be found using other geometric principles and formulas.

5. How do you find the measure of an angle in a triangle?

The measure of an angle in a triangle can be found by using the properties of triangles, such as the fact that the sum of the angles is always 180 degrees. Angles can also be found using trigonometric functions, such as sine, cosine, and tangent, in relation to the side lengths of the triangle.

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