Circle Geometry r Area = r 2 Reference Sheet Circumference = 2 r Cylinder Sector of Circle r circumference × central angle 2 central Arc Length = Rectangle Volume = rh angle 360º 2 Surface Area = 2rrh + 2 total area × central angle h r Sector Area = Area = lw Lateral Area = 2 rh 360º w Perimeter = 2lw + 2 l Trapezoid Sphere b1 Right Prism Area = –1 hb ( + b ) 4 3 2 12 Volume = – r h r 3 2 Volume = base area × h Surface Area =4 r Surface Area = base areas + face areas h Lateral Area = sum of face areas b2 Triangle Area = bh Cone h Volume = –1 rh2 s 3 Rectangular Solid 2 Surface Area + b h = rrs Lateral Area = rs r h Volume = lwh Parallelogram Surface Area = 2whwhll + 2 + 2 w Lateral Area = 2(lwh + ) h Area = bh Right Pyramid l b Volume = –1 × base area × h h 3 Pythagorean Theorem Surface Area = base area + face areas Trigonometry Formulas c abc222+= B b c a h DISTANCE BETWEEN a xx2 yy2 A C TWO POINTS: d=(–)+21 (–)21 b Cube xx+ yy+ Area =1 –ab sin C MID-POINT BETWEEN 12, 12 2 TWO POINTS: ( ) Volume = s 3 2 2 2 a b c Surface Area = 6s Law of sines: = = SUM OF INTERIOR ANGLES sin A sin B sin C 180 (n– 2) OF ANn -SIDED POLYGON: 222 s Law of cosines:ba = + c – 2 acB (cos ) The pairs of angles located inside the Alternate parallel lines (interior) and on opposite sides (alternate) of the transversal. Interior Angles These angles are congruent. ∠1 ≅ ∠2 푎푛푑 ∠3 ≅ ∠4 The pairs of angles located outside the Alternate parallel lines (exterior) and on opposite sides (alternate) of the transversal. Exterior Angles These angles are congruent. ∠1 ≅ ∠2 푎푛푑 ∠3 ≅ ∠4 The pairs of angles located inside the parallel lines (interior) and on the same Same Side side of the transversal. These angles Interior Angles are supplementary. 푚∠1 + 푚∠2 = 180 푎푛푑 푚∠3 + 푚∠4 = 180 The pairs of angles located outside the Same Side parallel lines (exterior) and on the same side of the transversal. These angles Exterior Angles are supplementary 푚∠1 + 푚∠7 = 180 These angles are opposite of each other in the same intersection. They share the same vertex. Vertical Angles They are congruent. ∠1 ≅ ∠2; ∠3 ≅ ∠4; ∠5 ≅ ∠6; ∠7 ≅ ∠8 These angles are in the same position Corresponding in different intersections. If you translated one intersection to the Angles other, the angles would correspond. They are congruent. Complementary These angles have a sum of 90°. They form a right angle. Angles 푚∠퐴퐵퐶 + 푚∠푃푄푅 = 90° Supplementary These angles have a sum of 180°. They form a straight line. Angles 푚∠퐴퐷퐶 + 푚∠퐶퐷퐵 = 180° .