Classify Triangles by Angles
Classify Triangles by Angles is a Grade 5 math skill from Illustrative Mathematics Chapter 7 (Shapes on the Coordinate Plane) that teaches four triangle classifications: acute (all angles less than 90°), right (one angle exactly 90°), obtuse (one angle greater than 90°), and equiangular (all angles exactly 60°). Students identify triangle types by examining their interior angles.
Key Concepts
Property Triangles can be classified by the size of their angles: An acute triangle has all three angles measuring less than $90^\circ$. A right triangle has one angle measuring exactly $90^\circ$. An obtuse triangle has one angle measuring greater than $90^\circ$. An equiangular triangle has all three angles measuring exactly $60^\circ$.
Examples A triangle with angles measuring $50^\circ, 60^\circ, 70^\circ$ is an acute triangle . A triangle with angles measuring $30^\circ, 60^\circ, 90^\circ$ is a right triangle . A triangle with angles measuring $40^\circ, 30^\circ, 110^\circ$ is an obtuse triangle . A triangle with angles measuring $60^\circ, 60^\circ, 60^\circ$ is an equiangular triangle .
Explanation Triangles can be classified based on the measures of their interior angles. If all three angles are acute (less than $90^\circ$), the triangle is an acute triangle. If one angle is a right angle (exactly $90^\circ$), it is a right triangle. If one angle is obtuse (greater than $90^\circ$), it is an obtuse triangle.
Common Questions
How do you classify triangles by their angles?
Examine the three interior angles. If all are less than 90°, it's acute. If one is exactly 90°, it's right. If one is greater than 90°, it's obtuse. If all three are exactly 60°, it's equiangular (a special acute triangle).
What is an acute triangle?
An acute triangle has all three interior angles measuring less than 90°. For example, a triangle with angles 50°, 60°, and 70° is acute. Every equilateral triangle is also acute.
What is the difference between obtuse and right triangles?
A right triangle has exactly one angle measuring 90°. An obtuse triangle has exactly one angle greater than 90°. Both can only have one such angle because the three angles must sum to 180°.
What chapter covers triangle classification in Illustrative Mathematics Grade 5?
Classifying triangles by angles is covered in Chapter 7 of Illustrative Mathematics Grade 5, titled Shapes on the Coordinate Plane.
What is an equiangular triangle?
An equiangular triangle has all three angles measuring exactly 60°. It is also equilateral (all sides equal). A triangle with angles 60°, 60°, and 60° is the only equiangular triangle possible.