The Elements of GeometryMacmillan, 1886 - 366 páginas |
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Página viii
... 110 . Vertical angles . PAGE ARTICLE 18 , 19 III . II . Angles about Two Points . PAGE . 19 112-113 . . 20 , 21 Transversal defined . . . Corresponding and alternate angles . 22 22 PAGE 119 . • 24 CHAPTER IV . PROBLEMS . viii CONTENTS .
... 110 . Vertical angles . PAGE ARTICLE 18 , 19 III . II . Angles about Two Points . PAGE . 19 112-113 . . 20 , 21 Transversal defined . . . Corresponding and alternate angles . 22 22 PAGE 119 . • 24 CHAPTER IV . PROBLEMS . viii CONTENTS .
Página 22
... Transversal . 112. If in a plane two lines are cut in two distinct points by a transversal , at each of the points four angles are deter- mined . 2/1 3/4 d Of these eight angles , four are between the two given lines ( namely , 4 , 3 ...
... Transversal . 112. If in a plane two lines are cut in two distinct points by a transversal , at each of the points four angles are deter- mined . 2/1 3/4 d Of these eight angles , four are between the two given lines ( namely , 4 , 3 ...
Página 48
... transversal , their alternate angles are unequal . 166. COROLLARY . If two lines cut by a transversal make corresponding angles equal , or interior or exterior angles on the same side of the transversal supplemental , the lines are ...
... transversal , their alternate angles are unequal . 166. COROLLARY . If two lines cut by a transversal make corresponding angles equal , or interior or exterior angles on the same side of the transversal supplemental , the lines are ...
Página 49
... transversal PC makes alternate angles equal ; CPD = 4 PCB , .. by 165 , PD is || AB . EXERCISES . 22. Draw , through a given point between two lines which are not parallel , a sect , which shall be terminated by the given lines , and ...
... transversal PC makes alternate angles equal ; CPD = 4 PCB , .. by 165 , PD is || AB . EXERCISES . 22. Draw , through a given point between two lines which are not parallel , a sect , which shall be terminated by the given lines , and ...
Página 50
... transversal cuts two parallels , it makes the alternate angles equal ; and therefore , by 113 , the corresponding angles are equal , and the two interior or two exterior angles on the same side of the transversal are supple- mental ...
... transversal cuts two parallels , it makes the alternate angles equal ; and therefore , by 113 , the corresponding angles are equal , and the two interior or two exterior angles on the same side of the transversal are supple- mental ...
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Términos y frases comunes
ABCD alternate angles altitude angles are equal angles equal angles opposite base bisect called chord circumcenter coincide common commutative law CONCLUSION construction COROLLARY cross-ratio describe diagonals diameter divided draw equal are congruent equal sects equiangular equivalent exterior angle figure given line given point given sect greater greatest common divisor hypothenuse HYPOTHESIS included angle inscribed inscribed angle intercepted interior intersecting lines isosceles triangle less locus magnitudes meet mid-point multiples number of sides pair parallelogram pass perigon perimeter perpendicular bisector plane MN prismatoid PROOF proportional quadrilateral radii radius ratio rectangle rectangle contained regular polygon respectively equal rhombus right angle Rule of Inversion sect joining segment sides equal sphere spherical polygon square straight angle subtended supplemental surface symmetrical tangent THEOREM THEOREM VIII three sides transversal triangles are congruent vertex
Pasajes populares
Página 44 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Página 112 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 24 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Página 190 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 101 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Página 266 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Página 13 - An Acute Angle is one which is less than a right angle.
Página 104 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Página 107 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.
Página 103 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.