classify the triangle according to side length and angle measure
Triangle ABC has side lengths of 6, 8, and 10 and angle measures of 30°, 60°, and 90°.
This triangle is an acute scalene triangle.
To classify a triangle according to side length and angle measure, we need to consider its sides and angles.
1. According to side length:
- Equilateral Triangle: All three sides are equal in length.
- Isosceles Triangle: Two sides are equal in length, and the third side is different.
- Scalene Triangle: All three sides have different lengths.
2. According to angle measure:
- Acute Triangle: All three angles are less than 90 degrees.
- Right Triangle: One angle is exactly 90 degrees.
- Obtuse Triangle: One angle is greater than 90 degrees.
Combining these classifications, we can have specific types of triangles:
- Equilateral and Equiangular Triangle: All sides are equal in length, and all angles are 60 degrees.
- Isosceles and Acute Triangle: Two sides are equal, and all angles are less than 90 degrees.
- Isosceles and Obtuse Triangle: Two sides are equal, and one angle is greater than 90 degrees.
- Scalene and Acute Triangle: All sides are different, and all angles are less than 90 degrees.
- Scalene and Obtuse Triangle: All sides are different, and one angle is greater than 90 degrees.
- Right Triangle: One angle is exactly 90 degrees. The sides can be equal or different in length.
Remember that a triangle can fall into multiple categories simultaneously. For example, an equilateral triangle is also an acute triangle.
To classify a triangle according to side lengths, we can use the following categories:
1. Based on Side Lengths:
- Equilateral Triangle: All three sides are equal in length.
- Isosceles Triangle: Two sides are equal in length.
- Scalene Triangle: All three sides have different lengths.
To classify a triangle according to angle measures, we can use the following categories:
2. Based on Angle Measures:
- Acute Triangle: All three angles are less than 90 degrees.
- Right Triangle: One angle is exactly 90 degrees.
- Obtuse Triangle: One angle is greater than 90 degrees.
By combining both classifications, we can describe a triangle using both its side lengths and angle measures. For example, a triangle can be classified as an equilateral and acute triangle, meaning all sides are equal in length and all angles are less than 90 degrees.