## A Shorter GeometryCUP Archive |

### Contents

Surface | 1 |

Direction | 11 |

SECOND STAGE | 22 |

Area by counting squaressquared paper | 23 |

Parallel Straight Lines | 29 |

More exact measurement by estimation | 40 |

Congruent Triangles | 49 |

Miscellaneous Exercises | 60 |

MISCELLANEOUS EXERCISES | 195 |

AREA OF CIRCLE | 202 |

MISCELLANEOUS EXERCISES | 211 |

Ratio and proportion | 219 |

CONSTRUCTION To find the fourth proportional to three | 225 |

CONSTRUCTION On a given straight line to construct | 232 |

AREAS OF SIMILAR FIGURES | 237 |

ii If AB CD two chords of a circle | 243 |

Book I | 75 |

CONTINUOUS CHANGE OF A FIGURE | 86 |

LOCI | 96 |

The locus of a point which is equidistant | 102 |

AREA OF PARALLELOGRAM | 117 |

To construct a triangle equivalent to | 124 |

THE THEOREM OF PYTHAGORAS | 128 |

Projections | 136 |

MISCELLANEOUS EXERCISES | 145 |

PRELIMINARY | 149 |

CONSTRUCTION To circumscribe a circle about a given | 155 |

CONSTRUCTION To inscribe a regular hexagon in a circle | 160 |

THE TANGENT | 166 |

ANGLES AT A POINT | 171 |

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

ANGLE PROPERTIES | 179 |

equal | 183 |

93 | 188 |

If a pair of opposite angles of a quadri | 189 |

ii The external bisector of an angle of | 249 |

If a straight line stands on another straight | 257 |

ANGLES OF A TRIANGLE A POLYGON | 265 |

INEQUALITIES | 273 |

297 | |

CHAP | 1 |

IV | 16 |

79 | 19 |

94 | 22 |

VI | 25 |

The Cylinder | 33 |

XI | 48 |

XII | 60 |

Coordinates in Space | 72 |

85 | 85 |

Perspective | 89 |

105 | |

109 | |

### Other editions - View all

### Common terms and phrases

AABC altitude angles are equal base BC bisects centimetres centre chord circle of radius circles touch circumcircle circumference common tangent concyclic Constr Construction Proof cyclic quadrilateral Data diagonal diameter distance divided Draw a circle Draw a straight drawn parallel drawn perpendicular edge equal circles equiangular equidistant equilateral triangle figure fixed point given angle given circle given line given point given straight line height hypotenuse inches interior angles intersect isosceles triangle LAOB LAPB length locus of points Measure meet mid-point miles opposite sides pair parallel to BC parallelogram plane Plot the locus polygon produced Prove quadrilateral ABCD radii ratio reflex angle Repeat Ex rhombus right angles right-angled triangle segment set square Show skew lines sphere subtended tetrahedron THEOREM tracing paper triangle ABC triangles are congruent vertex

### 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.