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ABCD adjoining altitude approaches base bisector bisects central chord circle circumference circumscribed coincide common congruent construct contains COROLLARY cutting described diagonals diameter difference divided Draw drawn ends equally distant equiangular equilateral triangle exterior angle external extremities feet figure Find Find the area formed four given circle given line given point greater half Hence hexagon homologous hypotenuse inches intercepted intersecting isosceles triangle length limit line joining mean measured median meeting midpoint NOTE opposite sides original pair parallel parallelogram perimeter perpendicular plane polygon PROBLEM produced Proof proportional PROPOSITION Prove quadrilateral radii radius ratio rectangle regular polygon Required respectively right angle right triangle secant segments sides similar square Statement straight line Substituting Suppose tangent THEOREM third trapezoid triangle equal unit vertex vertices
Page 144 - If the product of two quantities is equal to the product of two others, one pair may be made the extremes, and the other pair the means, of a proportion.
Page 4 - An angle is said to be included by its sides. An angle is bisected by a line drawn through the vertex and dividing the angle into two equal angles. TRIANGLES 23. A triangle is a portion of a plane bounded by three straight lines. These lines are the sides. The vertices of a triangle are the three points at which the sides intersect. The angles of a triangle are the three angles at the three vertices. Each side of a triangle has two angles adjoining it. The symbol for triangle is "A".
Page 41 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 173 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 53 - The line joining the mid-points of two sides of a triangle is parallel to the third side, and equal to half the third side.
Page 234 - The circumferences of two circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let R and R' be the radii of the circles, C and C" their circumferences, S and S' their areas. Inscribe in the two circles similar regular polygons ; let P and P...
Page 39 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.