## Elementary Geometry, Plane and Solid: For Use in High Schools and Academies |

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### Common terms and phrases

ABCD adjacent angles altitude angle formed base bisects called centre chord circular cone circumscribed coincide convex convex polygon Corollary Definition diagonals diameter dicular dihedral angle divided draw equal angles equiangular equidistant EXERCISES face angles figure frustum given circle given line-segment given plane given point given straight line greater Hence hypotenuse identically equal included angle inscribed interior angles isosceles triangle lateral area lateral edges lateral faces lateral surface length line parallel mid-point number of sides opposite sides pair parallel planes parallelogram pass perimeter perpen point of contact point of intersection polyhedron Proof Prop Proposition pyramid quadrilateral radii radius ratio rectangle regular polygon required to prove respectively right circular right triangle segment side BC similar slant height sphere spherical angle spherical polygon spherical triangle spherical units square subtended supplementary angle tangent tetrahedron theorem triangle ABC triangular prism trihedral unequal vertex volume

### Popular passages

Page 187 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 207 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.

Page 78 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.

Page 45 - Prove that, if two sides of a triangle are unequal, the angle opposite the greater side is greater than the angle opposite the less.

Page 231 - A polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a, pentagon; one of six sides, a hexagon ; one of seven sides, a heptagon ; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon.

Page 95 - 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 200 - The area of a triangle is equal to half the product of its base by its altitude.

Page 161 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.

Page 201 - Two parallelograms are similar when they have an angle of the one equal to an angle of the other, and the including sides proportional.

Page 29 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.