Preliminary three-dimensional geometry is the content of the first chapter of compulsory high school mathematics II, what are the knowledge points need to master? The following is my high school mathematics compulsory two three-dimensional geometry preliminary knowledge points, I hope it will help you.
High School Math Compulsory II Chapter 1 Preliminary three-dimensional geometryPrism surface area A = L * H + 2 * S, volume V = S * H
(L - perimeter of the base, H - height of the column, S - the area of the base)
Cylindrical surface area A = L * H + 2 * S = 2?*R * H + 2?*R^2, volume V = S * H = ? *R^2*H
(L - perimeter of the base, H - height of the column, S - area of the base, R - radius of the circle of the base)
Sphere surface area A=4?*R^2,volume V=4/3?*R^3
(R - radius of the sphere)
Cone surface area A=1/2*s*L+? *R^2,volume V=1/3*S*H=1/3?*R^2*H
(s - length of cone bus, L - perimeter of base, R - radius of base circle, H - height of cone)
Prismatic cone surface area A=1/2*s*L+S,volume V=1/3*S*H
(s - height of side triangles,L - perimeter of base. S - area of base,H - height of prism)
Perimeter of rectangle=(length+width)?2 Square a?side length C=4a
S=a2 Rectangle a and b-side lengths C=2(a+b)
S=ab Triangle a,b,c-triangle a,b,c-triangle lengths h-height of a side
s-half of perimeter A,B,C-inner angles where s =(a+b+c)/2 S=ah/2 =ab/2?sinC
[s(s-a)(s-b)(s-c)]1/2a2sinBsinC/(2sinA) Quadrilateral d,D-Diagonal length ? -Angle between diagonals S=dD/2?sin? Parallelogram a,b -Length of side h -Height of side a ? -Angle between two sides S=ah =absin?=
Rhombus a -Length of side ? -angle D-long diagonal length d-short diagonal length S=Dd/2
=a2sin? trapezium a and b-top and bottom base lengths h-height
m-median length S=(a+b)h/2 =mh d-diameter C=?d=2?r
S=?r2 =?d2/4 sector r? sector radius Perimeter of square = length of side?4 Area of rectangle = length? Area = length? Width
Area of square = side length? Length of side Area of triangle = base? height?2 Area of a parallelogram = base? Height
Area of trapezoid = (top base + bottom base)? Height?2 Diameter = radius?2 Radius = diameter?2 Circumference of a circle = pi? Diameter = Circumference? Radius?2 Area of circle = pi? radius? radius
Surface area of a rectangle = (length? width + length? height + width? height)?2 Volume of a rectangle = length? width? height Surface area of a square = prism length? Prong length?6 Volume of a square = Prong length? Prong length? Prism length Side area of cylinder = circumference of base circle? Height
Surface area of cylinder = area of upper and lower base + side area Volume of cylinder = area of base? Height
Volume of a cone = area of base? height?3 Volume of a rectangular (square, cylinder)
Volume of a rectangular (square, cylinder)
Volume of a rectangular (square, cylinder) = area of base? Height Plane figure Name Symbol Perimeter C and area S a?Degree of the central angle of the circle
C=2r+2?r?(a/360) S=?r2?(a/360)
Bow l-Arc length b-Strings length h-Height of the vector r-Radius ? -degree of the central angle of the circle S=r2/2?(? /180-sin?) = r2arccos[(r-h)/r] - (r-h)(2rh-h2)1/2
= ?r2/360 - b/2?[r2-(b/2)2]1/2
= r(l-b)/2 + bh/2
?2bh/3 Circled circle R-External radius r-Inner radius D- Diameter of outer circle d- Diameter of inner circle S=? (R2-r2)
=? (D2-d2)/4 Ellipse D-long axis d-short axis S=?Dd/4
Cubic Figures Name Symbol Area S and Volume V Square a-side length S=6a2 V=a3
Rectangular a-length b-width c-height S=2(ab+ac+bc)
V=abc Prism S- base area h-height V=Sh Prism S-base area <
h-height V=Sh/3 Prisms S1 and S2-upper and lower base area h-height V=h[S1+S2+(S1S1)1/2]/3
Proposed Column S1-upper base area S2-bottom area
S0-middle cross-sectional area h-height V=h(S1+S2+4S0)/6
Cylinder r-base radius h-height C? Perimeter of base
S bottom? Bottom area S side? Side area S surface? Surface area C=2?r S bottom =?r2
S side = Ch S table = Ch+2S bottom V=S bottom h =?r2h
Hollow cylinder R-radius of outer circle r-radius of inner circle
h-height V=?h(R2-r2) Straight cones r-bottom radius h-height V=?r2h/3
Circular table r-radius of upper bottom R-radius of lower base <
h-height V=?h(R2+Rr+r2)/3 ball r-radius
d-diameter V=4/3?r3=?d2/6 ball defect h-height of the ball defect r-radius of the ball
a-bottom radius of the ball defect V=?h(3a2+h2)/6 =?h2(3r-h)/3 a2=h(2r-h) table r1 and r2-both the top and bottom radius of the table
h-height V=? Bottom radius h-height V=?h[3(r12+r22)+h2]/6 Circular body R-radius of the ring
D-ring diameter r-radius of the ring cross section d-diameter of the ring cross section V=2?2Rr2 =?2Dd2/4
Bucket D-diameter of the bucket's belly D-diameter of the bottom of the bucket h-height of the bucket V=?h(2D2+d2)/12 (the center of the circle is center of the bucket). The center of the circle is the center of the barrel) V=?h(2D2+Dd+3d2/4)/15
(The bus is parabolic)
The rules of projection of three views are:
Main view, top view, length is correct
Main view, left view, height is equal
Left view, top view, width is equal
Relationship of points and lines
Axioms Axiom 1: If two points on a line are in a plane, then the line is in the plane
Axiom 2: If two planes have a common **** point, then they have a common **** line and all the common **** points are in the line
Axiom 3: Three points that are not **** lines define a plane
Corollary 1: A straight line and a point outside the line define a plane
Corollary 2: A line and a point outside the line define a plane.
Corollary 2: Two intersecting lines define a plane
Corollary 3: Two parallel lines define a plane
Axiom 4: Lines parallel to the same line are parallel
Definition of anisotropic straight line: two lines that are not parallel or intersecting
Determination Theorem: a line that passes through a point out of the plane and a point in the plane is an isotropic straight line, and a line that does not pass through the point in the plane is an isotropic straight line. are opposite straight lines.
Equal Angle Theorem: If two sides of an angle and two sides of another angle are parallel and in the same direction, then the two angles are equal
Line parallel? Line parallel If a line outside a plane is parallel to a line inside this plane, then this line is parallel to this plane. Lines are parallel? Line-parallel If a line is parallel to a plane and the plane through which it passes intersects this plane, then the line is parallel to the intersecting line.
Line-plane parallel? Face parallel If two intersecting lines in one plane are both parallel to another plane, then the two planes are parallel. Face parallel? Line parallel If two parallel planes intersect a third plane at the same time, then their intersecting lines are parallel.
Line perpendicular? A line is perpendicular to a plane if it is perpendicular to two intersecting lines in that plane. Line perpendicular? If two lines are perpendicular to a plane at the same time, then the lines are parallel.
Line perpendicular? A plane is perpendicular to another plane if it passes through a perpendicular line of the other plane.
Line perpendicular? Line perpendicular Line-plane perpendicular Definition: if a line a is perpendicular to a plane? any line in it is perpendicular, we say that line a is perpendicular to the plane?
Face perpendicular? Line perpendicular If two planes are perpendicular to each other, then a line perpendicular to their intersecting lines in one plane is perpendicular to the other plane.
Tripline Theorem If a line in a plane is perpendicular to a projection of the plane's blood into the plane, then the line is perpendicular to the diagonal.
High School Mathematics Compulsory II Chapter 1 Preliminary Examples of Stereo GeometryFor the tetrahedron ABCD, (1) if AB = AC, BD = CD how to prove that BC is perpendicular to AD?(2) If AB is perpendicular to CD and BD is perpendicular to AC, how to prove that BC is perpendicular to AD?
Proof:
(1). Take the midpoint F of BC,join AF,DF,then
∵AB=AC,BD=CD,
? △ABC and △DBC are isosceles triangles,
AF?BC,DF?BC. and AF?DF=F,
?BC?face AFD. and AD is in plane AFD,
?BC
(2). Let the projection of A on the face BCD be O. Join BO,CO,DO.Then
∵CD?AB,CD?AO,AB?AO=A,?CD?face ABO.
And BO is in the plane ABO,?BO?CD.
Similarly, DO?BC.Therefore, O is the pendant center of △BCD, so there is
CO? BD.
∵ BD?CO,BD?AO,CO?AO=O,?BD?Face AOC.