## 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 |

130 | 39 |

257 | 42 |

Congruent Triangles | 49 |

ARCS ANGLES CHORDS | 156 |

1 equal chords are equidistant from the centres | 163 |

CONSTRUCTION To draw the tangent to a circle at a given | 169 |

If two circles touch the point of contact lies | 175 |

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

AREA OF CIRCLE | 202 |

MISCELLANEOUS EXERCISES | 211 |

PAGE | 219 |

If two angles of a triangle are equal | 56 |

Miscellaneous Exercises | 60 |

Drawing to Scale | 66 |

Воок | 75 |

CONTINUOUS CHANGE OF A FIGURE | 86 |

SUBDIVISION OF A STRAIGHT LINE | 96 |

SYMMETRY | 106 |

Area by counting squaressquared paper | 114 |

AREA OF TRIANGLE | 120 |

Projections | 136 |

MISCELLANEOUS EXERCISES | 142 |

PRELIMINARY | 149 |

CONSTRUCTION To find the fourth proportional to three | 225 |

If in two triangles ABC DEF | 230 |

CONSTRUCTION On a given straight line to construct | 232 |

AREAS OF SIMILAR FIGURES | 237 |

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

ii The external bisector of an angle of | 249 |

lines | 262 |

Straight lines which are parallel to the same | 263 |

If two rightangled triangles have their | 272 |

REVISION PAPERS | 278 |

307 | |

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### Common terms and phrases

altitude base bearing bisector bisects Calculate called centre chord circle circumference congruent construct contained copy corresponding Data describe diagonal diameter distance divided Draw drawn edge equal equiangular equidistant equilateral triangle equivalent exercises Fact feet figure Find fixed point formed four Give given given line given point given straight line height inches inscribed intersect isosceles triangle length line joining locus mark mean Measure meet mid-point middle miles moves observed opposite sides pair parallel parallelogram pass perpendicular Plot polygon position produced Proof Prove quadrilateral ABCD radii ratio rectangle remaining respectively right angles right-angled triangle segment ship Show sides similar square straight line subtends taken THEOREM touch tracing 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.