## Plane Geometry |

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### Common terms and phrases

AABC ABCD acute angle adjoining figure altitude base bisect bisectors called central angle chord circular cone circumference circumscribed congruent construct Corollary corresponding cube cylinder diagonal diameter dihedral angles distance divide Draw drawn equiangular equilateral triangle EXERCISES feet frustum geometry given line given point Hence HINT hypotenuse inscribed interior angles intersection isosceles triangle lateral area lateral edges length locus lune measured middle point number of sides opposite Outline of proof parallel lines parallelepiped parallelogram perimeter perpendicular polyhedral angle polyhedron prism proportional prove pyramid quadrilateral radii radius ratio rectangle regular polygon regular polyhedrons rhombus right angles right circular right triangle ruler and compasses secant segment Show similar skew lines slant height solid sphere spherical polygon spherical triangle square straight line subtended surface tangent tetrahedron Theorem trapezoid triangle ABC triangular trihedral vertex vertices volume

### Popular passages

Page 182 - The area of a rectangle is equal to the product of its base and altitude ; that is, A = ab. 443. Corollary 1. The area of a square is equal to the square of its side. 444. Corollary 2. Tiro rectangles are to each other as the products of their bases and altitudes.

Page 58 - If two parallel lines are cut by a transversal, the alternate interior angles are equal.

Page 99 - Any two sides of a triangle are together greater than the third side.

Page 73 - If two triangles have two sides of the one equal to two sides of the...

Page 271 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. OM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'.

Page 329 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...

Page 74 - XVIII, prove that the perpendicular is the shortest line that can be drawn from a point to a straight line.

Page 103 - The Radius of a sphere is a straight line drawn from the center to any point in the surface.

Page 164 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 30 - Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.