Triangles • Topic 1 of 5

Classification of Triangles

Triangles are classified two ways: by sides and by angles. By sides, an equilateral triangle has three equal sides (and three 60° angles), an isosceles triangle has exactly two equal sides, and a scalene triangle has no equal sides. By angles, a triangle is acute (all angles below 90°), right (one 90° angle), or obtuse (one angle above 90°). The three angles always sum to 180°, so given two angles you can find the third by subtracting from 180. These classifications and the angle-sum rule are the foundation for nearly every triangle problem on the SAT.

Equilateral, isosceles and scalene triangles classified by sidesClassifying triangles by sides60°Equilateralall sides equalIsoscelestwo sides equalScaleneno sides equal

✅ Solved examples

1. Two angles of a triangle are 50° and 60°. Find the third.
180 − 50 − 60 = 70°.
2. A triangle has three equal sides. Classify it by sides.
Equilateral.
3. A triangle has one 90° angle. Classify it by angles.
Right triangle.
4. A triangle has exactly two equal sides. Classify it.
Isosceles.

✏️ Practice — try these, take hints as needed

1. Two angles are 40° and 75°. Find the third.
Angles sum to 180°.
180 − 40 − 75.
—
65°.
2. A triangle with no equal sides is called:
No sides equal.
—
—
Scalene.
3. A triangle with one angle above 90° is:
One obtuse angle.
—
—
Obtuse.
4. Each angle of an equilateral triangle measures:
180 ÷ 3.
—
—
60°.
5. Two angles are 90° and 45°. Find the third.
180 − 90 − 45.
—
—
45°.

📝 Topic test — 8 questions

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