## Practical Geometry |

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### Contents

MEASUREMENT OF LINES AND ANGLES | 1 |

SCALE DRAWING I not requiring the use of parallels | 13 |

PARALLEL STRAIGHT LINES | 20 |

ANGLES OF A TRIANGLE OF A POLYGON | 30 |

CONSTRUCTION OF TRIANGLES AND POLYGONS | 36 |

equal the triangles are congruent | 44 |

32 | 54 |

SCALE DRAWING III | 55 |

THE CIRCLE ANGLE PROPERTIES | 161 |

AREA OF CIRCLE | 175 |

Miscellaneous Exercises III | 183 |

SOLIDS OF UNIFORM CROSS | 197 |

THE CONE | 208 |

Plane and line at right angles p 212 Line inclined to plane | 214 |

THE SPHERE | 220 |

THE REGULAR SOLIDS | 226 |

Kite rhombus | 65 |

CONTINUOUS CHANGE OF A FIGURE | 71 |

the two given lines | 76 |

33 | 78 |

SIMILAR FIGURES | 86 |

triangles are similar | 92 |

the pantograph | 99 |

Area of similar figures The ratio of the areas of similar figures is equal to the square of the | 112 |

Miscellaneous Exercises II | 120 |

TAE CIRCLE ARCS | 135 |

THE CIRCLE TANGENTS | 146 |

CONTACT OF CIRCLES COMMON TANGENTS | 152 |

Revision Papers | 234 |

251 | |

THEOREMS | |

ANGLES AT A POINT | 2 |

If a straight line cuts two parallel straight lines | 8 |

i The opposite angles of a parallelogram are equal 21 | 21 |

Of all the straight lines that can be drawn to | 28 |

EXTENSION OF PYTHAGORAS THEOREM In an obtuse | 53 |

ii Conversely chords that are equidistant from the centres | 59 |

The tangent at any point of a circle and the radius | 60 |

If a straight line touch a circle and from the point | 66 |

### Common terms and phrases

ABCD altitude axis base bearing bisect bisector Calculate called centre chord circle circumference common cone congruent Construction containing copy corners corresponding Data describe diagonals diameter distance divided Draw drawn edge equal equidistant feet figure Find four Geometry Give given given point ground height Hence horizontal inches inscribed intersect isosceles triangle Join length locus mark mean Measure meet method mid-point miles moves Notes opposite sides pair parallel parallelogram pass perpendicular plane polygon position Practical produced Proof Prove pyramid quadrilateral radius ratio rectangle regular represents respectively RESULTS right angles scale segment ship Show sides similar sphere square straight line subtends surface symmetry taken tangent theorem touch triangle ABC turn vertex vertical volume yards

### Popular passages

Page xii - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.