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ABCD acute adjacent altitude arc BC base bisector bisects Book called centre cents chord circle circumference circumscribed coincide construct describe diagonals diameter divided Draw line drawn equal equally distant equilateral equivalent EXERCISES exterior extremities fall figure Find follows Given line given point greater Hence hypotenuse included inscribed intersecting isosceles triangle length less line joining manner mean measured meeting middle point number of sides one-half opposite sides parallel parallelogram passes perimeter perpendicular plane polygon PROBLEM produced Proof PROP proportional Prove quadrilateral radii radius ratio rectangle regular inscribed Required respectively right angles right triangle segments side BC similar square straight line surface tangent THEOREM third transversal trapezoid triangle ABC unit values vertex vertices
Page 222 - The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars.
Page 47 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Page 71 - A chord is a straight line joining the extremities of an arc ; as AB.
Page 149 - If one leg of a right triangle is double the other, the perpendicular from the vertex of the right angle to the hypotenuse divides it into segments which are to each other as 1 to 4.
Page 190 - 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 140 - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Page 161 - DB as often as possible. As the lines AD and DB are incommensurable, there must be a remainder, B'B, less than one of the equal parts. Draw B'C