## A Shorter GeometryCUP Archive |

### Contents

Surface | 1 |

Direction | 11 |

SECOND STAGE | 22 |

Parallel Straight Lines | 29 |

Angles of a Polygon | 37 |

Congruent Triangles | 49 |

Miscellaneous Exercises | 60 |

Drawing to Scale | 66 |

Ratio and proportion | 219 |

SIMILAR FIGURES | 226 |

CONSTRUCTION On a given straight line to construct | 232 |

BC | 233 |

RECTANGLE PROPERTIES | 240 |

CONSTRUCTION To describe a square equivalent to a given | 246 |

Playfairs Axiom | 261 |

ANGLES OF A TRIANGLE A POLYGON | 265 |

TABLE OF FACTS OR THEOREMS | 75 |

Book I | 84 |

Area by counting squaressquared paper | 90 |

COR If equal perpendiculars are erected on the same | 94 |

AREA OF PARALLELOGRAM | 117 |

CONSTRUCTION To construct a triangle equivalent to | 124 |

THE THEOREM OF PYTHAGORAS | 128 |

Projections | 136 |

MISCELLANEOUS EXERCISES | 145 |

PAGE | 149 |

CONSTRUCTION To circumscribe a circle about a given | 155 |

THE TANGENT | 166 |

CONSTRUCTION To inscribe a circle in a given triangle | 172 |

4 | 173 |

ANGLE PROPERTIES | 179 |

11 | 186 |

If a straight line touch a circle and from | 193 |

Common tangents to two circles | 199 |

FURTHER EXAMPLES OF LOCI | 205 |

MISCELLANEOUS EXERCISES | 211 |

INEQUALITIES | 273 |

23 | 286 |

297 | |

29 | 298 |

I | 1 |

40 | 13 |

79 | 19 |

98 | 23 |

VII | 27 |

124 | 28 |

The Cylinder | 33 |

184 | 44 |

224 | 50 |

233 | 51 |

246 | 57 |

257 | 58 |

266 | 60 |

Coordinates in Space | 72 |

Perspective | 89 |

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### Common terms and phrases

altitude base bisector bisects Calculate called centre chord circle circle of radius circumference common tangent congruent constant construct contained corresponding Data described diagonal diameter distance divided Draw drawn drawn parallel edge equal equiangular equidistant equilateral triangle equivalent externally fact figure Find fixed point formed four GEOMETRY Give given line given point given straight line height inches inscribed intersect isosceles triangle length locus mark mean Measure meet mid-point miles moves opposite sides pair parallel parallelogram pass perpendicular plane Plot polygon positions produced Proof proportional Prove quadrilateral ABCD radii radius ratio rectangle regular respectively right angles right-angled triangle segment Show sides similar square straight line subtended taken THEOREM third touch triangle ABC units vertex vertical

### Popular passages

Page xiii - In a right.angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle . . . . 130 Applications of Pythagoras' theorem . . . . 132 THEOREM 6.

Page xxi - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.

Page xi - The locus of a point which is equidistant from two intersecting straight lines consists of the pair of straight lines which bisect the angles between the two given lines.