Plane Geometry: And Supplements |
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Page 47
... Informal proof . Let A and B be any two points of line AB and C be any point that is not on AB . Then A , S P C A B M N A R C B B N M B , and C lie in one and only one plane ( SG 3 ) . All of A B lies in that plane ( SG 1 ) . Therefore ...
... Informal proof . Let A and B be any two points of line AB and C be any point that is not on AB . Then A , S P C A B M N A R C B B N M B , and C lie in one and only one plane ( SG 3 ) . All of A B lies in that plane ( SG 1 ) . Therefore ...
Page 104
... Informal proof . If AB were to intersect CD at a point O , then O would be in PNRM . But AB || PNRM . : . AB || CD . SG 26. If two parallel planes are cut by a third plane , the intersections are parallel . ( See Ex . 5 , p . 102 ...
... Informal proof . If AB were to intersect CD at a point O , then O would be in PNRM . But AB || PNRM . : . AB || CD . SG 26. If two parallel planes are cut by a third plane , the intersections are parallel . ( See Ex . 5 , p . 102 ...
Page 105
... Informal proof . Assume MN1 CD . Then AB 1 MN and EFM . ( SG 28 ) C A E N D B F Then AB || EF . ( Why ? ) M SG 30. If a straight line is perpen- dicular to one of two parallel planes , it is perpendicular to the other also . ( See Ex ...
... Informal proof . Assume MN1 CD . Then AB 1 MN and EFM . ( SG 28 ) C A E N D B F Then AB || EF . ( Why ? ) M SG 30. If a straight line is perpen- dicular to one of two parallel planes , it is perpendicular to the other also . ( See Ex ...
Contents
g The optional units from analytic geometry are included for three | 1 |
LinesAnglesPlanes | 11 |
W W | 24 |
Copyright | |
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ABCD acute angle adjoining figure altitude angle formed angles are equal apothem bisector bisects central angle chord conclusion congruent Construct converse coplanar corresponding sides diagonals diameter dihedral Draw drawn equal circles equidistant equilateral triangle exercises extended exterior angle figure for Ex Find frustum geometry given hypotenuse Hypothesis Informal proof inscribed intersect isosceles trapezoid isosceles triangle kind of angle lateral area length locus of points mean proportional measure meeting mid-point opposite sides parallel parallelogram perimeter perpendicular perpendicular-bisector Plan plane plane geometry Post postulate prism Prove pyramid quadrilateral radii radius ratio rectangle regular polygon rhombus right angle right circular right triangle secant segment similar sphere square Statements straight line Suggestion tangent theorem trapezoid trihedral angle vertex vertical angles Нур