## Plane and Solid Geometry |

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### Common terms and phrases

ABCDE ACē altitude apothem axis bisector bisects called centre chord circumference circumscribed coincide common construct curve denote diagonals diameter dihedral angles distance divided draw ellipse equidistant equilateral triangle equivalent face angles feet Find the area Find the locus frustum given circle given line given point given straight line given triangle greater Hence homologous homologous sides hypotenuse inches intersection lateral area lateral edges length limit middle point number of sides parallel planes parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism prismatoid Proof prove Q. E. D. PROPOSITION radii radius ratio rectangle regular polygon regular pyramid respectively right angle right circular right triangle secant segments similar slant height sphere spherical polygon spherical triangle square surface tangent tetrahedron THEOREM trapezoid triangle ABC triangular prism trihedral vertex vertices

### Popular passages

Page 44 - If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first 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 276 - If two planes are perpendicular to each other, a straight line drawn in one of them perpendicular to their intersection is perpendicular to the other plane.

Page 52 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.

Page 43 - If two angles of a triangle are unequal, the sides opposite are unequal, and the greater side is opposite the greater angle.

Page 193 - The areas of two triangles which have 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. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.

Page 362 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 171 - In any triangle the product of two sides is equal to the product of the diameter of the circumscribed circle by the altitude upon the third side.

Page 73 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.

Page 385 - Hence the two last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to the base, and bisects the vertical angle.

Page 77 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.