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Common terms and phrases
ABCD acute altitude Apply base bisector bisects called centre chord circle circumference circumscribed coincide common construct CONVERSELY describe diagonals diameter difference direction distance divide draw drawn equal equidistant equivalent extremities fall feet figure Find formed four given circle given line given point given straight line greater Hence homologous sides hypotenuse inches included increased indefinitely inscribed intercept intersecting legs length less limit mean measured meet middle points number of sides opposite sides parallel parallelogram passes perimeter perpendicular plane polygon PROBLEM Proof proportional PROPOSITION prove prove Proof radii radius ratio rectangle regular polygon right angle right triangle secant segments sides similar square straight line Suppose surface tangent THEOREM touch trapezoid triangle triangle ABC unit vertex vertices
Page 58 - The line which joins the middle points of two sides of a triangle is parallel to the third side, and is equal to half the third side.
Page 142 - If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA = Z A', and let AB : A'B' = AC : A'C'. To prove that the A ABC and A'B'C' are similar. In this case we prove the A similar by proving them mutually equiangular. Proof. Place the A A'B'C...
Page 128 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Page 153 - 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 diminished by twice the product of one of those sides and the projection of the other upon that side.
Page 126 - 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 39 - Two triangles are equal if two sides and the included angle of the one are equal, respectively, to two sides and the included angle of the other...
Page 30 - ... meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page 209 - 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 185 - The square constructed upon the difference of two straight lines is equivalent to the sum of the squares constructed upon these two lines, diminished by twice the rectangle of these lines.
Page 40 - 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...