Essentials of Plane Geometry |
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Common terms and phrases
AABC ABCD altitude angles are equal apothem arc AC base bisects called central angles chord circumference Corollary decagon diagonal diameter divide Draw drawn equal angles equal chords equal circles equal respectively equal sides equiangular equidistant equilateral triangle equivalent Exercises exterior angle Find the area Find the locus geometry given circle given equal given line segment given point Given the AABC Hence hypotenuse intersect isosceles triangle length line segment measured by arc midpoint number of sides opposite sides parallel lines parallelogram perimeter plane Post Problem produced Proposition Prove quadrilateral radii radius ratio rectangle reflex angle regular inscribed polygon regular polygon right angle right triangle secant similar polygons statement straight angle straight line student tangent Theorem third side transversal trapezoid triangle is equal vertex ZAOB
Popular passages
Page 234 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 59 - 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 182 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 102 - If two triangles have two sides of one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second...
Page 15 - 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 159 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Page 89 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 157 - The first and third terms are called the antecedents; the second and fourth terms, the consequents. The first and fourth terms are called the extremes; the second and third terms, the means. Thus in the proportion...
Page 192 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides increased by twice the product of one of those sides and the projection of the other upon that side.
Page 157 - To indicate that the ratio of A to B is equal to the ratio of C to D...