classify the triangle according to side length and angle measure
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.
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.