New Plane Geometry |
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Common terms and phrases
AB² ABC and A'B'C adjacent angles altitude angle formed angles are equal apothem approach the limit arc BC arcs intersecting bisector bisects central angle centre circumference circumscribed construct the triangle Converse of Prop divided Draw A ABC Draw line equal angles equal circles equal figures equal respectively equal sides equally distant equiangular equilateral triangle exterior angle Given line given point homologous sides hypotenuse intercepted arcs isosceles trapezoid isosceles triangle line CD line joining lines AC lines be drawn measured by arc meeting AC middle point number of sides one-half opposite sides parallelogram perimeter perpendicular polygon ABCDE Proof Prove quadrilateral radii radius rectangle regular inscribed regular polygon Required to construct rhombus right angles right triangle secant segments side BC sides are equal similar polygons subtended tangent THEOREM third side transversal trapezoid vertex
Popular passages
Page 50 - Two parallelograms are congruent if two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other.
Page 166 - S' denote the areas of two © whose radii are R and R', and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters.
Page 136 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.
Page 17 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 124 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.
Page 39 - If two angles of a triangle are equal, the sides opposite are equal.
Page 44 - 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, then the third side of the first is greater than the third side of the second.
Page 58 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 6 - C as a centre, and with a radius sufficiently great, describe an arc cutting the line AB in two points, A and B ; then, from...
Page 33 - That is, if two parallels are cut by a transversal, the sum of the interior angles on the same side of the transversal is equal to two right angles.