The lengths of two sides of a triangle are 15 inches each. The third side measures 10 inches. What type of triangle is this? Explain your answer using geometric terms.
Two sides are the same length so the triangle is isosceles.
To determine the type of triangle, we can analyze the lengths of its sides. In this case, the lengths given are 15 inches, 15 inches, and 10 inches.
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let's see if this condition is satisfied:
15 + 15 = 30, which is greater than 10.
Since the sum of the lengths of the two identical sides (15 + 15) is greater than the length of the third side (10), the triangle satisfies the triangle inequality theorem.
Based on the lengths of the sides, we can classify this triangle using geometric terms:
- Equilateral triangle: All three sides are of equal length.
- Isosceles triangle: Two sides are of equal length.
- Scalene triangle: All three sides have different lengths.
In this case, we have two sides of equal length (15 inches) and one side of a different length (10 inches). Thus, the triangle is classified as an isosceles triangle.
To determine the type of triangle, we need to consider the lengths of its sides. In this case, we have two sides of equal length (15 inches) and a third side of different length (10 inches).
Based on these lengths, we can classify the triangle using geometric terms:
1. Equilateral Triangle: An equilateral triangle has all three sides of equal length. Since only two sides of this triangle are equal in length, it is not an equilateral triangle.
2. Isosceles Triangle: An isosceles triangle has at least two sides of equal length. In this case, two sides of the triangle have a length of 15 inches, which makes it an isosceles triangle.
3. Scalene Triangle: A scalene triangle has all three sides of different lengths. Since the given triangle has two sides of equal length (15 inches) and one side of different length (10 inches), it is not a scalene triangle.
Therefore, the triangle in question is classified as an isosceles triangle.