Plane and Solid Geometry |
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Common terms and phrases
ABCD adjacent angles altitude angle formed angles are equal angles compare apothem arc intercepted base bisector bisects called central angle chord circle whose center circumference circumscribed compare in length Construct a triangle Data diagonals diameter dihedral angles distance divide equal circles equidistant equilateral triangle equivalent exterior extremities Find the locus frustum given line given point given straight line Hence homologous homologous sides hypotenuse inscribed angle interior angles intersecting isosceles trapezoid isosceles triangle line drawn measured by arc middle point number of sides opposite sides parallel lines parallelogram parallelopiped pass perimeter perpendicular plane prism produced Proof proportion prove pyramid Q.E.D. Proposition quadrilateral radii radius ratio rect rectangle formed regular polygon respectively rhombus right angles right triangle secant segment similar sphere spherical triangle subtended surface tangent Theorem transversal trapezoid triangle ABC triangles are equal trihedral vertex vertical angle
Popular passages
Page 103 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Page 147 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 65 - 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 45 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 62 - 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 59 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Page 81 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Page 45 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 31 - 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 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.