## A Shorter Geometry |

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### Contents

FIRST STAGE | 1 |

Direction | 11 |

SECOND STAGE | 22 |

Parallel Straight Lines | 29 |

132 | 34 |

Angles of a Polygon | 37 |

Congruent Triangles | 49 |

If two angles of a triangle are equal | 56 |

PAGE | 219 |

CONSTRUCTION To find the fourth proportional to three | 225 |

CONSTRUCTION On a given straight line to construct | 232 |

AREAS OF SIMILAR FIGURES | 237 |

PARALLEL STRAIGHT LINES | 259 |

ANGLES OF A TRIANGLE A POLYGON | 265 |

If two rightangled triangles have their | 272 |

EXAMINATION PAPERS | 278 |

Miscellaneous Exercises | 60 |

Drawing to Scale | 66 |

Воок | 75 |

CONTINUOUS CHANGE OF A FIGURE | 86 |

CONSTRUCTION To draw a straight line parallel to a given | 95 |

SYMMETRY | 106 |

PAGE | 114 |

AREA OF TRIANGLE | 120 |

Projections | 136 |

A a+b kak + | 143 |

PRELIMINARY | 149 |

CONSTRUCTION To circumscribe a circle about a given | 155 |

In equal circles or in the same circle | 158 |

Lengths of chords | 164 |

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

ANGLE PROPERTIES | 179 |

E al32 a+ba | 187 |

MISCELLANEOUS EXERCISES | 195 |

AREA OF CIRCLE | 202 |

MISCELLANEOUS EXERCISES | 211 |

297 | |

CHAP PAGE I Planes and Lines 1 | 1 |

Parallel positions of Planes and Lines 7 | 7 |

Perpendicular positions of Lines and Planes 11 | 11 |

Oblique positions of Planes and Lines 16 | 16 |

Skew Straight Lines 20 | 20 |

Loci 25 | 25 |

The Prism 27 | 27 |

The Cylinder 33 | 33 |

The Pyramid 37 | 37 |

The Cone 44 | 44 |

The Sphere 48 | 48 |

The Solid Angle 60 | 60 |

The Regular Solids the Principle of Duality Eulers Theorem 65 | 65 |

Coordinates in Space 72 | 72 |

Plan and Elevation 75 | 75 |

Perspective 89 | 89 |

MISCELLANEOUS EXERCISES | 93 |

105 | |

107 | |

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### Common terms and phrases

ABCD altitude base bisector bisects Calculate called centre chord circle circumference common congruent construct contained copy corresponding Data describe diagonals diameter distance divided Draw drawn edge elevation ends equal equidistant faces Fact feet figure Find fixed point formed four Give given given line given point given straight line height inches inscribed intersect isosceles triangle length locus mark mean Measure meet mid-point miles moves opposite sides pair parallel parallelogram pass perpendicular plane polygon position prism produced projection Proof proportional Prove pyramid quadrilateral radius ratio rectangle regular respectively right angles right-angled triangle round segment Show sides similar solid sphere square straight line subtends surface taken tangent THEOREM touch tracing triangle ABC vertex vertical volume

### 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.