Plane and Solid Geometry |
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Page 17
... ABCD , prove that AC = BD . 29. If four points , A , B , C , D , are placed in order on a line , and if ACBD , prove that AB CD . 30. To test a carpenter's " square , " draw a line AB , and from a point P on AB draw a perpendicular to ...
... ABCD , prove that AC = BD . 29. If four points , A , B , C , D , are placed in order on a line , and if ACBD , prove that AB CD . 30. To test a carpenter's " square , " draw a line AB , and from a point P on AB draw a perpendicular to ...
Page 21
... ABCD , ABDA , and diagonal AC bisects = B BAD , prove A that BC CD , and that AC bisects DCB . 32. Show that the distance BA across a lake may be measured by setting up a stake at O , sighting across it to fix the lines A'B and B'A ...
... ABCD , ABDA , and diagonal AC bisects = B BAD , prove A that BC CD , and that AC bisects DCB . 32. Show that the distance BA across a lake may be measured by setting up a stake at O , sighting across it to fix the lines A'B and B'A ...
Page 28
... ABCD is a quadrilateral of which DA is the longest side and BC the shortest . Which is greater , ZB or ZD ? Prove it . [ Suggestion : Draw BD . ] Also C or LA ? Prove it . Theorem 7. If two angles of a triangle are unequal 28 PLANE ...
... ABCD is a quadrilateral of which DA is the longest side and BC the shortest . Which is greater , ZB or ZD ? Prove it . [ Suggestion : Draw BD . ] Also C or LA ? Prove it . Theorem 7. If two angles of a triangle are unequal 28 PLANE ...
Page 53
... ABCD . that ( 1 ) A + B = st . 2 , ( 2 ) A = ZC . Proof . 1. A + B = st . Z , which 2 . 3 . 4 . proves ( 1 ) . Th . 17 , cor . 2 ZB + C st .. ZA + ZB = ZB + ZC . ..ZA / C , which proves ( 2 ) . Why ? Why ? Why ? COROLLARY . If one angle ...
... ABCD . that ( 1 ) A + B = st . 2 , ( 2 ) A = ZC . Proof . 1. A + B = st . Z , which 2 . 3 . 4 . proves ( 1 ) . Th . 17 , cor . 2 ZB + C st .. ZA + ZB = ZB + ZC . ..ZA / C , which proves ( 2 ) . Why ? Why ? Why ? COROLLARY . If one angle ...
Page 54
... ABCD . To prove ( 1 ) A ABC ACDA , ( 2 ) AB = DC . Proof . 1. In the figure , x = x ' , and 2 . y = y ' . Th . ( ? ) A AC AC . 3. .. A ABC = ACDA , which pr 4. ... ABDC , which proves Similarly for diagonal BD , and sides B COROLLARIES ...
... ABCD . To prove ( 1 ) A ABC ACDA , ( 2 ) AB = DC . Proof . 1. In the figure , x = x ' , and 2 . y = y ' . Th . ( ? ) A AC AC . 3. .. A ABC = ACDA , which pr 4. ... ABDC , which proves Similarly for diagonal BD , and sides B COROLLARIES ...
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Common terms and phrases
a₁ ABCD altitude angles equal b₁ b₂ bisect bisectors called central angle chord circle circumcenter circumference circumscribed cone congruent construct convex COROLLARIES corresponding cylinder DEFINITIONS diagonals diameter dihedral angle divided draw drawn edges equal angles equal bases equidistant equilateral EXERCISES face angles figure of th frustum geometry given line given point greater Hence hypotenuse inscribed interior angles intersection isosceles lateral area line-segment lune mid-points oblique opposite sides orthocenter parallel lines parallelogram perigon perimeter perpendicular plane polar polyhedral angle polyhedron prism prismatic space Prismatoid produced Proof pyramid quadrilateral radii radius ratio rectangle rectangular parallelepiped regular regular polygon respectively rhombus right angle segments Similarly slant height sphere spherical polygon spherical surface spherical triangle square straight angle straight line Suppose symmetric tangent tetrahedron Theorem transverse section trihedral vertex vertices volume
Popular passages
Page 90 - The projection of a point on a line is the foot of the perpendicular from the point to the line. Thus A
Page 24 - The third side is called the base of the isosceles triangle, and the equal sides are called the sides. A triangle which has no two sides equal is called a scalene triangle. The distance from one point to another is the length of the straight line-segment joining them. The distance from a point to a line is the length of the perpendicular from that point to that line. That this perpendicular is unique will be proved later. This is the meaning of the word distance in plane geometry. In speaking of...
Page 295 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Page 74 - Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Page 107 - XLI. 2. The perpendicular bisector of a chord passes through the center of the circle and bisects the subtended arcs.
Page 37 - If two triangles have two sides of the one respectively equal to two sides of the other, and the contained angles supplemental, the two triangles are equal.
Page 225 - Theorem. If each of two intersecting planes is perpendicular to a third plane, their line of intersection is also perpendicular to that plane. Given two planes, Q, R, intersecting in OP, and each perpendicular to plane M. To prove that OP _L M.
Page 265 - A Plane Surface, or a Plane, is a surface in which if any two points are taken, the straight line which joins these points will lie wholly in the surface.
Page 159 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 94 - To construct a parallelogram equal to a given triangle and having one of its angles equal to a given angle.