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ABē ABCD ACē altitude bisector bisects centre circumference circumscribed circle coincide construct a square describe an arc diagonal diameter draw equal arcs equal respectively equiangular equiangular polygon equidistant equilateral polygon equilateral triangle exterior angle feet Find the area given angle given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches indefinitely diminished intersecting isosceles trapezoid isosceles triangle legs line joining mean proportional measured by arc middle points number of sides obtuse parallel parallelogram perimeter perpendicular PROBLEM prove Proof Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rectangle regular inscribed regular polygon rhombus right angle right triangle SCHOLIUM secant segments shortest side similar polygons square equivalent subtended tangent THEOREM third side trapezoid triangle ABC vertex vertices
Page 46 - 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. Given A ABC and A'B'C ' with Proof STATEMENTS Apply A A'B'C ' to A ABC so that A'B
Page 148 - 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 187 - Two triangles having 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.
Page 64 - 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.
Page 134 - 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 158 - The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.
Page 132 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion in which the other two are made the means.
Page 45 - 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 36 - ... meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.