## 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 find the fourth proportional to three | 225 |

Proportional compasses | 236 |

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

ii The external bisector of an angle of | 249 |

If a straight line stands on another straight | 257 |

AnGles of a trianGle a polyGon | 265 |

Inequalities | 273 |

297 | |

Table of facts or theorems | 75 |

Continuous change of a figure | 86 |

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

The locus of a point which is equidistant | 102 |

Area by counting squaressquared paper | 114 |

Area of trianGle | 120 |

The theorem of PythaGoras | 128 |

Projections | 136 |

A a + bkak + bk | 142 |

PAgE | 149 |

Construction To circumscribe a circle about a given | 155 |

In equal circles or in the same circle | 163 |

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

AnGles at a point | 171 |

Angle properties | 179 |

Miscellaneous exercises | 195 |

Area of circle | 202 |

Miscellaneous exercises | 211 |

Ratio and proportion | 219 |

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 |

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 Eulert Theorem 65 | 65 |

Coordinates in Space 72 | 72 |

Plan and Elevation 75 | 75 |

Perspective 3 c 89 | 89 |

Miscellaneous Exercises 93 | 93 |

Answers 105 | 105 |

107 | |

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### Common terms and phrases

altitude angles are equal base BC bisector bisects centimetres centre chord circle of radius circles touch circumcircle circumference common tangent cone cyclic quadrilateral Data diagonal diameter distance Draw a straight drawn parallel drawn perpendicular equal circles equiangular equidistant equilateral triangle figure Find fixed point geometry given circle given line given point given straight line height horizontal hypotenuse inches interior angles intersect isosceles triangle ITEx length line joining locus of points Measure meet mid-point miles opposite sides pair parallel to BC parallelogram plan and elevation plane Plot the locus polygon prism produced Prove pyramid quadrilateral ABCD radii ratio rectangle reflex angle rhombus right angles right-angled triangle segment set square Shew Show similar triangles skew lines solid angle sphere subtended surface tetrahedron Theorem tracing paper triangle ABC vertex

### 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.