## Schultze and Sevenoak's Plane and Solid Geometry |

### From inside the book

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**prove**that 21 = 24 . Ex . 81. If 21 is the supplement of ≤2 , and ≤3 is the supplement of 22 , why is 21 = 23 ? PROPOSITION I. THEOREM 53. Vertical angles are equal . Given the vertical 1 and 2 . To**prove**3 2 21 = 22 .**Proof**3 ... Page 23

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**prove**△ ABCAA'B'C ' . STATEMENTS**Proof**REASONS Place A ABC upon △ A'B'C ' so that AB shall coincide with A'B ' . Then BC will take the di- rection B'C ' . AC will take the direction A'C ' . .. C will fall upon c ' . ... .AABC = AA'B'C ... Page 25

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**prove**A ABCAA'B'C ' . STATEMENTS**Proof**REASONS Place A ABC upon A A'B'C ' so that BC shall coincide with B'C ' . BA will take the direction of B'A ' , The point 4 will fall upon the point 4 ' , .. AC will coincide with A'C ' . .. AABCAA ... Page 29

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**prove**ECBD . * Ex . 127. Hyp . 21 = 22 , DB1 AC , and CE LAD , To**prove**LC = LD . B 5 Ex . 128. Hyp . AB = AE , 25 ...**proof**is left to the student . ] 72. COR . 1. The base angles of an isosceles. LINES AND RECTILINEAR FIGURES 29. Page 31

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**proved**by means of Prop . IV ( compare § 121 ) . Ex . 144 Ex . 145 Ex . 146 A A D ' D Ex . 147 Ex . 144. If ABC and ADC are ...**prove**AABCA A'B'C ' . 113 44**Proof**STATEMENTS Suppose no side longer than BC LINES AND RECTILINEAR FIGURES 31.### 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 LAOB lateral area lateral edge line joining locus median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism produced PROPOSITION prove Proof pyramid Q. E. D. Ex quadrilateral radii ratio rectangle reflex angle regular polygon respectively equal rhombus right angles right triangle segments sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal trihedral vertex angle vertices

### 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 222 - 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 192 - 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 208 - 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 177 - 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 188 - 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 409 - 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...