## Plane and Solid Geometry |

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### Common terms and phrases

ABCD adjacent angles altitude angle formed angles are equal angles compare apothem bisector bisects called chord circumference circumscribed compare in length cone of revolution cylinder of revolution Data diagonals diameter dihedral angles distance divide Draw equal circles equidistant equilateral triangle exterior extremities face angles FGHJK frustum given line given point given triangle Hence homologous homologous sides hypotenuse inscribed angle intercepted interior angles intersecting isosceles triangle lateral edges middle point number of sides opposite sides parallel lines parallelogram pass a plane perimeter polyhedral angle polyhedron prism produced Proof prove pyramid Q.E.D. Proposition quadrilateral radii radius ratio rect rectangle formed rectangular parallelopiped regular polygon respectively rhombus right angles right triangle secant segment slant height sphere spherical polygon spherical triangle subtended tangent tetrahedrons Theorem third side transversal trapezoid triangle ABC triangles are equal trihedral vertex vertical angle volume

### Popular passages

Page 67 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.

Page 46 - Any exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Page 64 - From 56 and 57 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other...

Page 47 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...

Page 124 - DE and on the same side of it ; but equal triangles on the same base, and on the same side of it, are between the same parallels ; [I.

Page 33 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.

Page 27 - The perpendicular is the shortest line that can be drawn from a point to a straight line.

Page 215 - The. sum of the angles of any polygon is equal to twice as many right angles as the polygon has sides, less four right angles.

Page 134 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.

Page 88 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.