Segments with the lengths of 6, 8, and 10 units will form what type of triangle?
A right triangle because 6^2 + 8^2 = 100 and the square root of 100 is 10 :)
See if the Pythagorean Theorem works.
To determine the type of triangle formed by segments with lengths 6, 8, and 10 units, we can apply the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
So, let's check if this condition is satisfied for the given segments:
1. Sum of the lengths of segments with lengths 6 and 8 units: 6 + 8 = 14.
2. Length of the remaining segment (10 units).
Since 14 is greater than 10, the triangle inequality theorem is satisfied for these segments.
Now, to determine the type of triangle, we need to consider the lengths of the sides:
- If all three sides of a triangle have the same length, it is an equilateral triangle.
- If two sides of a triangle have the same length, it is an isosceles triangle.
- If all three sides have different lengths, it is a scalene triangle.
In this case, the lengths of the segments are 6, 8, and 10 units, which are all different. Therefore, the segments will form a scalene triangle.