## A Shorter Geometry |

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### Contents

FIRST STAGE | 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 |

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

79 | 178 |

ANGLE PROPERTIES | 179 |

SECTION IX | 187 |

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

MISCELLANEOUS EXERCISES | 199 |

FURTHER EXAMPLES OF LOCI | 205 |

Ratio and proportion | 219 |

BOOK I | 75 |

To draw a straight line perpendicular to a given straight | 83 |

If one pair of adjacent sides of a parallelogram | 89 |

Area by counting squaressquared paper | 90 |

3 A quadrilateral is a parallelogram if both pairs | 93 |

AREA OF PARALLELOGRAM | 117 |

CONSTRUCTION To construct a triangle equivalent to | 124 |

THE THEOREM OF PYTHAGORAS | 128 |

Projections | 136 |

118 | 140 |

A a+b kak+bk | 142 |

PRELIMINARY | 149 |

CONSTRUCTION To circumscribe a circle about a given | 155 |

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

THE TANGENT | 166 |

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### Common terms and phrases

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

### 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.