Schultze and Sevenoak's Plane and Solid Geometry |
From inside the book
Results 1-5 of 40
Page 31
Arthur Schultze, Frank Louis Sevenoak. Ex . 143. In the preceding diagram , if DE = EF = FD , and LAFD = ∠ BDE = ∠ CEF , then △ ABC is equilateral . NOTE . The equality of angles is sometimes proved by means of Prop . IV ( compare ...
Arthur Schultze, Frank Louis Sevenoak. Ex . 143. In the preceding diagram , if DE = EF = FD , and LAFD = ∠ BDE = ∠ CEF , then △ ABC is equilateral . NOTE . The equality of angles is sometimes proved by means of Prop . IV ( compare ...
Page 52
... Prop . XIII . ] E A B 1 C 2 F D Given parallel lines AB and CD , and the alt . int . 1 and 2 . To prove STATEMENTS 1 ... diagram , if AB 52 PLANE GEOMETRY.
... Prop . XIII . ] E A B 1 C 2 F D Given parallel lines AB and CD , and the alt . int . 1 and 2 . To prove STATEMENTS 1 ... diagram , if AB 52 PLANE GEOMETRY.
Page 53
... diagram , if AB || CD , and AD || BC , then ∠ B = ∠ D. PROPOSITION XIX . THEOREM A 3 2 B 4 C D 106. If two parallel lines are cut by a transversal , the corresponding angles are equal . [ Converse of Prop . XIV . ] E 1 A B 3 2 C D F ...
... diagram , if AB || CD , and AD || BC , then ∠ B = ∠ D. PROPOSITION XIX . THEOREM A 3 2 B 4 C D 106. If two parallel lines are cut by a transversal , the corresponding angles are equal . [ Converse of Prop . XIV . ] E 1 A B 3 2 C D F ...
Page 55
... Prop . XV . ] C A B + 23 D Given AB || CD , and the int . 1 and 2 , lying on the same side of a transversal . To ... diagram , if ED || AB , AC = CD , and EB and AD are st . lines , ABC CDE . C 1/2 B E D C A B C Ex . 240. If the ...
... Prop . XV . ] C A B + 23 D Given AB || CD , and the int . 1 and 2 , lying on the same side of a transversal . To ... diagram , if ED || AB , AC = CD , and EB and AD are st . lines , ABC CDE . C 1/2 B E D C A B C Ex . 240. If the ...
Page 70
... diagram given here , AC > BC , AD | AC , and B DBBC . Prove BD > AD . D Ex . 323. Prove Prop . XXX directly . HINT . At B draw angle CBD = ∠ C. Ex . 320 A C D Ex . 322 B Ex . 324. The sum of the altitudes of a triangle is less than ...
... diagram given here , AC > BC , AD | AC , and B DBBC . Prove BD > AD . D Ex . 323. Prove Prop . XXX directly . HINT . At B draw angle CBD = ∠ C. Ex . 320 A C D Ex . 322 B Ex . 324. The sum of the altitudes of a triangle is less than ...
Other editions - View all
Common terms and phrases
altitude angle equal angle formed angles are equal annexed diagram bisect bisector chord circumference circumscribed congruent cylinder diagonals diagram for Prop diameter dihedral angles divide draw drawn equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inscribed intersecting isosceles triangle lateral area lateral edge line joining median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism produced Proof PROPOSITION prove pyramid Q. E. D. Ex quadrilateral radii ratio rectangle reflex angle regular polygon respectively equal rhombus right angles right triangle segments similar sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal trihedral vertex angle vertices Εχ Нур
Popular passages
Page 82 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 220 - 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 190 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 206 - The area of a rectangle is equal to the product of its base and altitude.
Page 67 - If two sides of a triangle are unequal, the angles opposite are unequal, and the greater angle is opposite the greater side.
Page 175 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 25 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.
Page 70 - 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 186 - Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
Page 407 - 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...