A Text-book of Geometry
Ginn & Company, 1892 - Geometry, Plane - 437 pages
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ABCD acute altitude Apply base bisector bisects called centre chord circle circumference circumscribed coincide common construct contained describe diagonal diameter difference distance divide draw drawn equal equidistant equilateral equivalent exterior extremities fall feet figure Find formed four given circle given line given point given straight line greater Hence homologous sides hypotenuse inches indefinitely inscribed intercept intersecting isosceles joining legs length less limit mean measured meet middle point parallel parallelogram passes perimeter perpendicular polygon PROBLEM Proof proportional PROPOSITION prove prove Proof quantities radii radius ratio rectangle regular polygon respectively right angle right triangle secant segments shortest sides similar similar polygons square straight line Suppose tangent THEOREM touch triangle triangle ABC unit 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.
Page 156 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.