Triangle Properties — SAT Math Explained
Fundamental characteristics of triangles including angle sum, side relationships, and classifications by angles and side lengths.
The Core Idea
Every triangle, regardless of shape or size, obeys the same fundamental laws. The most powerful: all interior angles always sum to exactly 180°. This constraint alone enables solving for unknown angles.
Key Properties
All three interior angles of any triangle sum to 180°
The sum of any two sides must be greater than the third side
An exterior angle equals the sum of the two non-adjacent interior angles
Classification By Angles
All three angles less than 90°
Exactly one 90° angle
Exactly one angle greater than 90°
Classification By Sides
All three sides different lengths (all angles also different)
Exactly two sides equal (the angles opposite the equal sides are also equal)
All three sides equal (all angles = 60°)
Pythagorean Theorem
For right triangles: a² + b² = c², where c is the hypotenuse (side opposite the right angle)
Common Pythagorean Triples
3-4-5, 5-12-13, 8-15-17, 7-24-25 — and any multiples thereof (6-8-10, 9-12-15, etc.)
Common Errors to Avoid
Applying the Pythagorean theorem to non-right triangles
Using a leg instead of the hypotenuse as c in a² + b² = c²
Adding all three sides for area instead of using base × height / 2
Practice: Triangle Properties
5 SAT-style questions. Select your answer and get an instant explanation.
Interior angles of a triangle sum to:
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