Geometry & Trigonometry • 15% of test
Triangles
Select your difficulty level to start practicing. We recommend mastering each level before moving to the next.
Beginner5 Sets
Beginner Practice
Start here to build your foundation. Clear problems and straightforward calculations.
Target Score
400-550
Intermediate5 Sets
Intermediate Practice
Level up with more complex equations and multi-step problems.
Target Score
550-700
Advanced3 Sets
Advanced Practice
Master the hardest concepts. Complex word problems and abstract applications.
Target Score
700-800
What is Triangles?
Triangle questions test the Pythagorean theorem, special right triangles, similarity, and triangle properties including area.
Step-by-Step Strategy
⚠️ Common Traps to Avoid
Frequently Asked Questions
When can I use the Pythagorean theorem?
Only for RIGHT triangles. The hypotenuse (longest side) is opposite the right angle.
How do I use special right triangles?
Identify if it's 30-60-90 or 45-45-90 from angles, then use the ratios to find unknown sides.
What makes triangles similar?
Same angles (AA), or proportional sides (SSS), or one angle and proportional adjacent sides (SAS).
How do I find the height?
Height is perpendicular to the base. For non-right triangles, you may need to draw an altitude.
What is the triangle inequality?
Any side < sum of others. Practice side-relationship problems in our <a href='/math'>SAT Math practice library</a>.
Are proofs tested?
No formal proofs, but you need to understand why properties work to apply them correctly.
What is the 'Angle Sum' property?
The interior angles of any triangle always add up to exactly 180 degrees. This is fundamental for finding missing angles.
How do I identify 'Equilateral' and 'Isosceles' triangles?
Equilateral triangles have three equal sides and 60° angles. Isosceles have at least two equal sides and two equal base angles.
What is the 'Exterior Angle' theorem?
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
How do I find the area of an equilateral triangle?
Area = (s²√3) / 4, where s is the side length. This is a very helpful shortcut to memorize!
What are 'Pythagorean Triples'?
Integer side lengths for right triangles like 3-4-5, 5-12-13, and 8-15-17. Recognizing these saves massive time.
Does similarity only apply to right triangles?
No. Any two triangles are similar if they have proportional sides and equal angles, regardless of their specific type.
What is the 'SAS' rule for area?
Area = ½ab·sin(C), where a and b are sides and C is the included angle. Useful when you don't know the perpendicular height.
How do I find the distance between two points using triangles?
Create a right triangle where the distance is the hypotenuse. The horizontal and vertical changes are the legs.
What if a triangle is inside another triangle?
Look for shared angles. Refine your similarity skills with our <a href='/math/geometry/intermediate'>Intermediate Geometry practice</a>.