Classify the triangle according to side length and angle measurement.
isosceles; right
• equilateral; obtuse
• scalene; acute
• scalene; right
• isosceles; acute
The given classifications of triangles are as follows:
1. Isosceles; right triangle: This means that two sides of the triangle are equal in length, and one angle measures exactly 90 degrees.
2. Equilateral; obtuse triangle: This indicates that all three sides of the triangle are equal in length, and one angle measures greater than 90 degrees.
3. Scalene; acute triangle: In this case, all three sides of the triangle have different lengths, and all three angles are less than 90 degrees.
4. Scalene; right triangle: This classification implies that all three sides of the triangle are of different lengths, and one angle measures exactly 90 degrees.
To classify a triangle according to its side length and angle measurement, you need to understand the definitions of different types of triangles:
1. Equilateral Triangle: All sides and angles of an equilateral triangle are equal. Therefore, all angles in an equilateral triangle are 60 degrees. If a triangle has equal side lengths and an obtuse angle, it cannot be equilateral, as an obtuse angle does not exist in an equilateral triangle. Thus, "equilateral; obtuse" is not a valid classification.
2. Isosceles Triangle: An isosceles triangle has two sides of equal length. If the triangle has two equal sides and a right angle (90 degrees), it is classified as an isosceles right triangle or "isosceles; right".
3. Scalene Triangle: A scalene triangle has all sides of different lengths. If the triangle has different side lengths and all angles less than 90 degrees, then it is classified as a scalene acute triangle or "scalene; acute".
4. Right Triangle: A right triangle has one angle measuring 90 degrees. If a triangle has one right angle, regardless of its side lengths, it is classified as a right triangle. If the right triangle has no sides of equal length, it is further classified as a "scalene; right" triangle.
Based on the given options, the correct classification is "scalene; right".