Classifying by the largest angle
Grade 4 students classify triangles by their largest angle in Saxon Math Intermediate 4. A triangle is a right triangle if its largest angle equals exactly 90°, an obtuse triangle if the largest angle exceeds 90°, and an acute triangle if all three angles are less than 90°. Students find the unknown angle using the rule that angles sum to 180°—if two angles are 25° and 45°, the third is 180° − 70° = 110°, making it an obtuse triangle. The critical rule: always classify by the largest angle, not just any single angle.
Key Concepts
One way to classify a triangle is by referring to its largest angle as either obtuse, right, or acute. An obtuse angle is larger than a right angle. An acute angle is smaller than a right angle.
A triangle with angles of $30^{\circ}$, $60^{\circ}$, and $90^{\circ}$ is a right triangle. A triangle with angles of $20^{\circ}$, $40^{\circ}$, and $120^{\circ}$ is an obtuse triangle. An equilateral triangle with three $60^{\circ}$ angles is also an acute triangle.
Look at a triangle's biggest angle to give it a name! If the largest angle is a perfect corner ($90^{\circ}$), it's a right triangle. If it's wider than that (more than $90^{\circ}$), it's an obtuse triangle. If all three angles are sharp and smaller than a right angle, it's an acute triangle. The largest angle defines its class.
Common Questions
How do you classify a triangle by its largest angle?
If the largest angle is exactly 90°, it is a right triangle. If the largest angle is greater than 90°, it is an obtuse triangle. If even the largest angle is less than 90° (meaning all angles are acute), it is an acute triangle.
What do the three angles of any triangle always add up to?
The three interior angles of any triangle always sum to 180°. Use this rule to find an unknown third angle by subtracting the sum of the two known angles from 180.
Can a triangle have more than one obtuse angle?
No. Since the three angles must sum to 180°, having two angles greater than 90° would require their sum to exceed 180°, which is impossible. A triangle can have at most one obtuse angle.
How is a right triangle identified?
A right triangle has exactly one angle of 90°, shown by a small square in the corner. The side opposite the right angle is the longest side, called the hypotenuse.
What is the most common mistake when classifying triangles?
Classifying the triangle based on a non-largest angle. For example, a triangle with angles 120°, 30°, and 30° has two acute angles but is classified as obtuse because its largest angle (120°) is greater than 90°.
What are real examples of each triangle type?
A right triangle appears in a set square or the corner of a rectangular room. An obtuse triangle looks like a wide, flat slice. An equilateral triangle with three 60° angles is a perfect example of an acute triangle.