## Essentials of Solid Geometry |

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### Common terms and phrases

altitude base called chord circle circular cone circumscribed common compute cone cone of revolution congruent Consider construct Corollary corresponding cube cubic cylinder determine diagonal diameter dihedral angles dimensions distance divided Draw drawn edges equal equilateral equivalent Exercises faces figure Find the area Find the volume follows formed formula four frustum geometry given given line greater Hence included inscribed intersection lateral area lateral edges lateral faces length lune measured meet oblique opposite parallel parallel planes pass perpendicular plane polar pole polyhedral angles polyhedron prism projection Proof proportional Proposition Prove pyramid radii radius regular pyramid respectively segment shown shows sides similar Similarly slant height solid sphere spherical spherical triangle square straight line student surface symmetric tangent tetrahedron Theorem third total surface triangle triangular trihedral unit vertex vertices volume zone

### Popular passages

Page 7 - The line joining the midpoints of two sides of a triangle is parallel to the third side and equal to one-half of it.

Page 40 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.

Page 176 - 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.

Page 10 - 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. Given A ABC and A'B'C...

Page 15 - 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 77 - The height of a cone is the perpendicular distance from the vertex to the plane of the base.

Page 3 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.

Page 24 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.

Page 16 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 15 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.