SAT Math · Study & Practice

Triangles

Triangles are the most tested shape on the SAT. This chapter covers classifying triangles, congruence, similarity, the Pythagorean theorem and the two special right triangles. Read each topic, work the problems with the hint ladder, then take the 8-question topic test.

Topics

1 Classification of Triangles 4 worked · 5 practice · 8-Q test Start → 2 Triangle Congruence 4 worked · 5 practice · 8-Q test Start → 3 Similar Triangles 4 worked · 5 practice · 8-Q test Start → 4 Pythagorean Theorem 4 worked · 5 practice · 8-Q test Start → 5 Special Right Triangles 4 worked · 5 practice · 8-Q test Start →

Chapter test

📝 Triangles — Chapter Test

25 fresh questions · timed · full solutions

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Formula Reference Sheet

This chapter

Core facts

Angle sum	the three angles add to 180°
Pythagorean theorem	a² + b² = c² (right triangles)
Similarity	corresponding sides are in the same ratio

Special right triangles

45-45-90	legs equal; hypotenuse = leg × √2
30-60-90	sides in ratio 1 : √3 : 2
Common triples	3-4-5, 5-12-13, 8-15-17

Digital SAT reference

Area & Circumference

Circle area	A = πr²
Circle circumference	C = 2πr
Rectangle	A = ℓw
Triangle	A = ½ b h

Volume

Rectangular box	V = ℓwh
Cylinder	V = πr²h
Sphere	V = 4⁄3 πr³
Cone	V = 1⁄3 πr²h
Pyramid	V = 1⁄3 ℓwh

Right triangles

Pythagorean theorem	a² + b² = c²
30°–60°–90°	sides x : x√3 : 2x
45°–45°–90°	sides s : s : s√2

Constants

Degrees in a circle	360°
Radians in a circle	2π
Angles of a triangle	sum = 180°