Plane and Solid Geometry |
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Page 26
... altitude upon the hypotenuse of a right triangle divides the right angle into two parts , which are respectively ... altitudes upon the arms of an isosceles triangle are equal . PROPOSITION XIII . THEOREM 100. An exterior angle of ...
... altitude upon the hypotenuse of a right triangle divides the right angle into two parts , which are respectively ... altitudes upon the arms of an isosceles triangle are equal . PROPOSITION XIII . THEOREM 100. An exterior angle of ...
Page 28
... equal . Ex . 106. The vertical angle of an isosceles triangle is : ( 1 ) 40 ° ; ( 2 ) m ° . Find the angle formed by the base , and an altitude upon an arm . Ex . 107. If an arm of an isosceles triangle 28 PLANE GEOMETRY.
... equal . Ex . 106. The vertical angle of an isosceles triangle is : ( 1 ) 40 ° ; ( 2 ) m ° . Find the angle formed by the base , and an altitude upon an arm . Ex . 107. If an arm of an isosceles triangle 28 PLANE GEOMETRY.
Page 32
... altitude upon one arm of one triangle are equal respectively to one angle and the altitude upon one arm of the other . * Ex . 127. If the opposite sides of a quadrilateral are equal , the diagonals bisect each other . Ex . 128. Two ...
... altitude upon one arm of one triangle are equal respectively to one angle and the altitude upon one arm of the other . * Ex . 127. If the opposite sides of a quadrilateral are equal , the diagonals bisect each other . Ex . 128. Two ...
Page 33
... altitude upon one of them of one triangle are respectively equal to two sides and the homologous altitude of the other . Ex . 132. If the perpendiculars from the midpoint of one side of a tri- angle upon the two other sides are equal ...
... altitude upon one of them of one triangle are respectively equal to two sides and the homologous altitude of the other . Ex . 132. If the perpendiculars from the midpoint of one side of a tri- angle upon the two other sides are equal ...
Page 50
... altitude of a parallelogram or trapezoid is the perpendicular distance between the two bases . PROPOSITION XXXII . THEOREM 134. The opposite sides and angles of a parallelo- gram are equal . A B Нур . D ABCD is a parallelogram . To ...
... altitude of a parallelogram or trapezoid is the perpendicular distance between the two bases . PROPOSITION XXXII . THEOREM 134. The opposite sides and angles of a parallelo- gram are equal . A B Нур . D ABCD is a parallelogram . To ...
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Common terms and phrases
ABCD altitude angles are equal bisect bisector chord circumference circumscribed cone construct a triangle cylinder diagonals diagram for Prop diameter diedral angles divide draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle face angles find a point Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inches inscribed intersecting isosceles triangle joining the midpoints lateral area lateral edges line joining mean proportional median opposite sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN point equidistant polyedral angle polyedron PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segments sphere spherical polygon spherical triangle square straight angle straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex
Popular passages
Page 148 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 150 - If, from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.
Page 180 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 337 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes ; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Page 312 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...
Page 149 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.
Page 328 - Every section of a sphere made by a plane is a circle.
Page 257 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.