## Essentials of Solid Geometry |

### Common terms and phrases

AABC ABC and A'B'C altitude altitude h angles are equal axis bisects called chord circle circumscribed cone of revolution congruent conic surface Consider Ex Corollary corresponding cube cubic diagonal diameter dihedral angles distance Draw equivalent Exercises face angles Find the area Find the volume formed formula frustum given line given point Hence inches inscribed intersection isosceles lateral area lateral edges lateral faces line segment locus of points lower base measuring number of degrees oblique opposite parallel planes parallelogram perimeter perpendicular plane geometry plane passing pole polyhedral angles Proof Proposition Prove radii rectangular parallelepiped regular polygon regular polyhedrons regular pyramid right angles right circular cylinder Similarly slant height sphere of radius spherical degrees spherical excess spherical polygon spherical triangle straight line tangent tetrahedron Theorem third side total surface triangular prism trihedral upper base vertex vertices 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.