## A Shorter Geometry |

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### Contents

FIRST STAGE | 1 |

Direction | 11 |

SECOND STAGE | 22 |

117 | 24 |

135 | 26 |

Parallel Straight Lines | 29 |

Angles of a Polygon | 37 |

118 | 47 |

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

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

MISCELLANEOUS EXERCISES | 211 |

235 | 212 |

PAGE | 219 |

CONSTRUCTION To find the fourth proportional to three | 225 |

AREAS OF SIMILAR FIGURES | 237 |

PARALLEL STRAIGHT LINES | 259 |

Congruent Triangles | 49 |

Miscellaneous Exercises | 60 |

Drawing to Scale | 66 |

120 | 71 |

BOOK I | 75 |

CONTINUOUS CHANGE OF A FIGURE | 86 |

Area by counting squaressquared paper | 90 |

SUBDIVISION OF A STRAIGHT LINE | 96 |

SYMMETRY | 106 |

AREA OF PARALLELOGRAM | 117 |

AREA OF POLYGON | 124 |

If a triangle and a parallelogram stand | 127 |

Projections | 136 |

MISCELLANEOUS EXERCISES | 145 |

PRELIMINARY | 149 |

ARCS ANGLES CHORDS | 156 |

In equal circles or in the same circle | 158 |

THE TANGENT | 166 |

ANGLES AT A POINT | 171 |

CONTACT OF CIRCLES | 174 |

If the line joining two points subtends | 186 |

ANGLES OF A TRIANGLE A POLYGON | 265 |

INEQUALITIES | 273 |

297 | |

PAGE | 1 |

Perpendicular positions of Lines and Planes | 11 |

Skew Straight Lines | 20 |

96 | 22 |

sired by half | 26 |

The Prism | 25 |

140 | 32 |

The Cylinder | 33 |

169 | 37 |

The Pyramid | 40 |

181 | 43 |

195 | 46 |

The Sphere | 48 |

243 | 54 |

The Solid Angle | 60 |

Coordinates in Space | 72 |

MISCELLANEOUS EXERCISES | 93 |

105 | |

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### Common terms and phrases

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