高二数学-.棱柱与棱锥(二)(b版)(High school mathematics -. prism and pyramid (two) (b Edition)).doc
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1、高二数学-9.9棱柱与棱锥(二)(b版)(High school mathematics -9.9 prism and pyramid (two) (b Edition))9.9 prisms and pyramids (two)Learning guidance1. to solve the problems in the pyramid, we should first clear the definition and related properties of pyramid, especially some intrinsic properties of the pyramidThe
2、three angles, the three distances, the area and the volume of the 2. pyramids are always through them. Through the proof and calculation of them, the true grasp of the pyramids is achievedKey points of knowledgeDefinition of the 1 pyramid of knowledgeOne of the faces is polygonal, and the rest of th
3、e faces are triangles with a common vertex. The closed geometry enclosed by these faces is called a pyramidThe definition of a regular pyramid: the bottom surface is a regular polygon, and the projection of the vertex at the bottom is the center of the base plane. The pyramid is called a regular pyr
4、amidThe properties of 2 pyramid of knowledge(1) high, and slant on the bottom surface of the slant pyramid projective form a triangle pyramid; high lateral and lateral ribs on the bottom surface of the projective form a right triangle; the side edge and the bottom edge of ofbending pyramid, (part of
5、) a right triangle in the bottom of the pyramid; slant projection in the side edge and the bottom, the bottom surface of the projection (part) to form a right triangle. (Figure 9 - 9 - 55: Rt VDH, Rt VAH, Rt VAD, Delta Delta Delta Rt HAD) calculation. That is often in the pyramid above four right an
6、gled triangle, is especially important.(2) using a frustum of a plane parallel to the base plane, the cross section is similar to the base, and some of the sides are proportional, and the area is proportional to the square of the corresponding edge(3) it is especially pyramid, each side edge is equa
7、l, each side are congruent isosceles triangleSpecial knowledge in Section 3 Pyramid: diagonal plane (section two is not adjacent to the side edge are parallel to the bottom surface of the section).Side area formula of 4 pyramid of knowledge pointThe drawing of horizontal horizontal drawing of 5 stra
8、ight pyramid of knowledge point: oblique two measuring methodRelative concepts and properties of knowledge points, 6 polyhedra and regular polyhedraEspecially regular polyhedron, it has and only five kinds (namely, regular tetrahedron, regular hexahedron, positive eight body, positive twelve body, p
9、ositive twenty body)Knowledge point 7 uses the properties of pyramids to study the relation between the lines and lines, lines and planes, planes and planes, and calculates the distances, the three angles and the area and volume of the pyramidsProblem solving methods and skills trainingThe proof and
10、 calculation of the relation between the line and the line in the 1 pyramidFigure 9956 in 1 cases, four pyramid PABCD, bottom ABCD is a right angled trapezoid, angle BAD = 90 degrees, AD = BC, AB = BC = a, AD = 2A, PA, ABCD and PD face the bottom surface, the bottom surface at an angle of 30 degrees
11、.(1) if the AE group PD, E group: BE PD pedal, confirmation;(2) the different surface lines AE and CD into the corner.analysis careful analysis is not difficult to find graphic features, PA, BA and DA 22 are perpendicular to each other, which is the establishment of the coordinate system, to provide
12、 the conditions of solid geometry problem is transformed into a vector, in order to find the easy way to give you one.proof (1) take A as the origin, and AB, AD and AP take the line as the coordinate axis, and establish the Cartesian coordinate systemPD group of AB and R, t AE PD dreams,PD BE. * t(2
13、) dreams of anomalous PA surface ABCD, PD and the bottom surface at an angle of 30 degrees,L / PDA = 30 E, EF t AD, AE pedal F = A / EAF = 60 deg,I (1) in solving the problem with vector, to choose the coordinate system, find out the coordinates of the point, write the vector coordinates. (2) in sol
14、ving the problems concerned with pyramid, should make full use of the definition and character of the pyramid, and if the pyramid on the surface of the point, line, space tend to figure the problem of plane.The proof and calculation of the relation between the line and the surface in the 2 pyramid2
15、cases of known: four PABCD pyramid, the bottom surface is a right angled trapezoid, which AB, CD, BA t AD, PAD t side bottom ABCD, (1): confirmation of anomalous PCD plane PAD plane; (2) if AB = 2, CD = 4, PBC is equal to the positive side of the long side of the triangle 10 the AC and PCD for the d
16、iagonal side angle sine value.(1) analysis it is proved that the plane and the plane are vertical. Generally, the judgment theorem of the line and the surface is verticalprove dreams quadrilateral ABCD right angled trapezoid, CD. AB saidAnd the dreams of anomalous PAD bottom ABCD surface, a bottom s
17、urface PAD ABCD = AD,AD group AB, AB group of PAD. star(2) analysis we should grasp the projection angle for line and plane anglesolution by (1), PAD group and PAD PCD, a plane surface PCD = PD. * PAD in the surface in A AH group PD. H. AH group of pedal PCD (theorem vertical surface). Then connect
18、to CH, then ACH for front line, face the angles (Figure 9 - 9 - 61).I line and plane angle grasping projective.Determine the projective points depends on nature theorem of vertical surface. The vertical line and surface vertical is often use each other and transform into each other.The proof and cal
19、culation of the relation between the plane and the surface in the 3 pyramid3 cases in figure 9966, ABCD AB t BCD tetrahedron, plane, BC = CD / BCD = 90 / ADB = 30 degrees, E degrees, F, AC, AD respectively is the midpoint.(1): confirmation of anomalous BEF plane ABC plane;(2) calculate the angle of
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