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ABCD acute adjacent altitude approaches base bisector bisects called centre chord circle circumference circumscribed coincide common constant construct describe diagonals diameter difference distance divide Draw drawn equal equidistant equilateral triangle equivalent exterior external extremities fall feet figure Find formed given circle given line given point greater half Hence hypotenuse inches included inscribed intercepted intersecting isosceles triangle joining legs length less limit locus mean measured meet middle point number of sides parallel parallelogram passes perimeter perpendicular plane PROBLEM Proof proportional PROPOSITION prove quantities radii radius ratio rectangle regular polygon respectively right angle right triangle segments sides similar square straight line supplementary Suppose tangent THEOREM touch trapezoid triangle triangle ABC true unequal variable vertex vertices zero
Σελίδα 94 - Any two sides of a triangle are together greater than the third side.
Σελίδα 42 - If two triangles have two sides of the 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.
Σελίδα 191 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.
Σελίδα 156 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 75 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Σελίδα 71 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.
Σελίδα 38 - Two triangles are equal if the three sides of the one are equal respectively to the three sides of the other. In the triangles ABC and A'B'C', let AB = A'B', AC = A'C', BC=B'C'. To prove A ABC= A A'B'C'. Proof. Place A A'B'C' in the position AB'C, having its greatest side A'C' in coincidence with its equal AC, and its vertex at B', opposite B ; and draw BB'.
Σελίδα 55 - 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 46 INTERCEPTS BY PARALLEL LINES.
Σελίδα 50 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.