Plane Geometry Summary

ACT Math · Axiom Academy

SUMMARY Plane Geometry Unit Summary Angles, triangles, quadrilaterals, circles, polygons, and 3D figures — the largest geometry topic on the ACT, reviewed in one pass. Plane geometry is the highest-value topic on the ACT — roughly 23% of the Math Test (about 14 questions), so mastering it is one of the best study investments you can make. A handful of angle facts do most of the work: vertical angles are equal, a straight line's angles sum to , a triangle's interior angles sum to , and parallel lines make corresponding and alternate interior angles equal. The Pythagorean theorem a^2+b^2=c^2 and its common triples (3-4-5, 5-12-13, 8-15-17, 7-24-25) — plus the 45-45-90 and 30-60-90 ratios — unlock most triangle and length problems without a calculator. Area, perimeter, circumference, and volume all reduce to picking the right formula and plugging in ; the recurring trap is using a diameter as a radius or a slant side as the perpendicular height. Complex figures come apart into simple ones: break a composite shape into rectangles, triangles, and circles, then add or subtract their areas. Angles & Lines Angle Relationships Intersecting and parallel lines create predictable, equal, or supplementary angle pairs — the foundation for every figure that follows. Vertical angles: formed by intersecting lines, always congruent (equal). Supplementary angles: two angles that sum to ; linear pairs are always supplementary. Complementary angles: two angles that sum to .

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