## A Shorter GeometryCUP Archive |

### Contents

Surface | 1 |

Direction | 11 |

SECOND STAGE | 22 |

PRELIMINARY | 28 |

Parallel Straight Lines | 29 |

Angles of a Polygon | 37 |

Miscellaneous Exercises | 60 |

TABLE OF FACTS OR THEOREMS | 75 |

ANGLES AT A POINT | 171 |

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

ANGLE PROPERTIES | 179 |

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

MISCELLANEOUS EXERCISES | 195 |

To construct an interior common tangent to two circles | 201 |

MISCELLANEOUS EXERCISES | 211 |

Ratio and proportion | 219 |

To draw the perpendicular bisector of a given straight line | 81 |

PARALLELOGRAMS | 87 |

The locus of a point which is equidistant | 101 |

90 | 105 |

MISCELLANEOUS EXERCISES | 107 |

Area by counting squaressquared paper | 114 |

AREA OF TRIANGLE | 120 |

Equivalent triangles which have equal bases | 126 |

THE THEOREM OF PYTHAGORAS | 128 |

Projections | 136 |

MISCELLANEOUS EXERCISES | 145 |

COR A straight line drawn through the midpoint of | 153 |

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

THE TANGENT | 166 |

94 | 225 |

AH | 226 |

If two triangles have one angle of the | 235 |

i The internal bisector of an angle of | 248 |

If a straight line stands on another straight | 257 |

If straight lines are drawn from a point | 264 |

INEQUALITIES | 273 |

96 | 293 |

Drawing to Scale | 299 |

307 | |

308 | |

311 | |

Heights and Distances | |

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### Common terms and phrases

AABC altitude angles are equal base BC bisects Calculate centimetres centre chord circle of radius circles touch circumcircle circumference common tangent concyclic Constr construct a triangle Construction Proof cuts BC cyclic quadrilateral diagonal diameter divided Draw a circle drawn parallel equal circles equiangular equidistant equilateral triangle figure find a point fixed point Freehand given angle given circle given line given point given straight line hypotenuse inches interior angles intersect isosceles triangle LAPB length line joining locus of points Measure meet mid-point miles opposite sides parallel straight lines parallel to BC parallelogram Plot the locus polygon produced Pythagoras quadrilateral ABCD radii ratio reflex angle Repeat Ex rhombus right angles right-angled triangle segment set square Show similar triangles subtends THEOREM tracing paper trapezium triangle ABC vertex

### Popular passages

Page xi - 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 ix - 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.

Page xvi - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.