ACT Math · 23% of the test
Plane Geometry
Plane Geometry covers triangles, polygons, circles, parallel lines and angles, areas and perimeters, and basic three-dimensional figures.
What's actually tested
Plane Geometry is the second-largest content category on the ACT math section. Items range from quick angle-chase problems to multi-step area and volume computations.
Subtopics
Click any subtopic to see filed practice questions, worked solutions, and a short tactical guide.
Triangles and the Pythagorean theorem
Right triangles, similar triangles, and triangle inequalities.
Polygons, perimeter, and area
Quadrilaterals, regular polygons, and area formulas.
Circles, arcs, and chords
Circumference, area, arcs, sectors, and inscribed angles.
Three-dimensional figures
Volume and surface area of prisms, cylinders, and cones.
Sample practice questions in this topic
- Easy Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 6 and 8. What is the length of the hypotenuse?
- Easy Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 6 and 8. What is the length of the hypotenuse?
- Medium Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 7 and 24. What is the length of the hypotenuse?
- Medium Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 5 and 12. What is the length of the hypotenuse?
- Medium Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 9 and 12. What is the length of the hypotenuse?
- Hard Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 8 and 15. What is the length of the hypotenuse?
- Easy Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 8 and 15. What is the length of the hypotenuse?
- Easy Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 5 and 12. What is the length of the hypotenuse?
- Medium Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 3 and 4. What is the length of the hypotenuse?
- Medium Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 9 and 12. What is the length of the hypotenuse?
- Medium Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 8 and 15. What is the length of the hypotenuse?
- Hard Triangles and the Pythagorean theorem In a right triangle, the two legs have lengths 5 and 12. What is the length of the hypotenuse?
See all 56 questions in Plane Geometry →
How students lose points here
Confusing diameter with radius, applying the Pythagorean theorem in non-right triangles, and forgetting that interior angles of a triangle sum to 180°. The good news: nearly every common mistake on this topic comes from one of three or four recurring patterns. Spend an hour reviewing those patterns and your accuracy on this topic typically jumps two or three percentage points immediately, which on a balanced test is worth ten to twenty scaled score points depending on your band.
How to study this topic
Memorize the formula sheet on this site. Plane Geometry rewards recognition: knowing which formula applies in three seconds saves you ten on every item. A reasonable session looks like fifteen practice items, untimed, with you reading the worked solution after every one — even the questions you got right, because being right by accident teaches nothing. After two or three such sessions, attempt a timed mini-set of ten items. If your accuracy stays above 80%, move on. If it doesn't, drill the lowest-accuracy subtopic for another session before you push forward.