Identify each triangle based on their angles as right, acute, obtuse, and equiangular. 1. A triangle with angles 70°, 50°, and 60°. 2. A triangle with a 90° angle. 3. A triangle with angles 30°, 110°, and 40°. 4. A triangle with angles 60°, 60°, and 60°. 5. A triangle with angles 130°, 25°, and 25°.
Answer (1)
To identify the type of triangles based on their angles, it's important to understand the definitions:
Right Triangle : A triangle with one 90° angle.
Acute Triangle : A triangle where all angles are less than 90°.
Obtuse Triangle : A triangle with one angle greater than 90°.
Equiangular Triangle : A triangle where all three angles are equal and each angle is 60°.
Now, let's analyze each given triangle:
Triangle with angles 70°, 50°, and 60° :
Since all angles are less than 90°, this triangle is an Acute Triangle .
Triangle with a 90° angle :
Since it contains a 90° angle, this is a Right Triangle .
Triangle with angles 30°, 110°, and 40° :
This triangle has an angle of 110°, which is greater than 90°. Therefore, it is an Obtuse Triangle .
Triangle with angles 60°, 60°, and 60° :
All angles are 60°, making this an Equiangular Triangle (and also equilateral, since all sides are equal when all angles are equal in a triangle).
Triangle with angles 130°, 25°, and 25° :
This triangle has an angle of 130°, which makes it an Obtuse Triangle .
These classifications help determine the properties and relationships within each type of triangle, which can be useful in solving various geometric problems.
