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Page x
... pair of adjacent sides of a parallelogram are equal , all its sides are equal Rectangle , square , rhombus , trapezium A theorem and its converse 8825 89 90 92 THEOREM 23. ( 1 ) A quadrilateral is a parallelogram X CONTENTS - BOOK I.
... pair of adjacent sides of a parallelogram are equal , all its sides are equal Rectangle , square , rhombus , trapezium A theorem and its converse 8825 89 90 92 THEOREM 23. ( 1 ) A quadrilateral is a parallelogram X CONTENTS - BOOK I.
Page xi
... pair of opposite sides are equal and parallel . PAGE 93 93 · ( 3 ) A quadrilateral is a parallelogram if both pairs of opposite sides are equal · • ( 4 ) A quadrilateral is a parallelogram if its diagonals bisect one another • COR . If ...
... pair of opposite sides are equal and parallel . PAGE 93 93 · ( 3 ) A quadrilateral is a parallelogram if both pairs of opposite sides are equal · • ( 4 ) A quadrilateral is a parallelogram if its diagonals bisect one another • COR . If ...
Page xvi
... pair of opposite angles of a quadri- lateral are supplementary , its vertices are concyclic The locus of points ( on one side of a given straight line ) at which the line subtends a constant angle is an arc of a circle , the given line ...
... pair of opposite angles of a quadri- lateral are supplementary , its vertices are concyclic The locus of points ( on one side of a given straight line ) at which the line subtends a constant angle is an arc of a circle , the given line ...
Page xix
... pair of alternate angles are equal , or ( 2 ) a pair of corresponding angles are equal , or ( 3 ) a pair of interior angles on the same side of the cutting line are together equal to two right angles , then the two straight lines are ...
... pair of alternate angles are equal , or ( 2 ) a pair of corresponding angles are equal , or ( 3 ) a pair of interior angles on the same side of the cutting line are together equal to two right angles , then the two straight lines are ...
Page xxii
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Contents
Surface | 1 |
Direction | 11 |
SECOND STAGE | 22 |
PRELIMINARY | 28 |
Parallel Straight Lines | 29 |
Angles of a Polygon | 37 |
Miscellaneous Exercises | 60 |
TABLE OF FACTS OR THEOREMS | 75 |
ANGLES AT A POINT | 171 |
CONSTRUCTION To inscribe a circle in a given triangle | 172 |
ANGLE PROPERTIES | 179 |
If a pair of opposite angles of a quadri | 189 |
MISCELLANEOUS EXERCISES | 195 |
To construct an interior common tangent to two circles | 201 |
MISCELLANEOUS EXERCISES | 211 |
Ratio and proportion | 219 |
To draw the perpendicular bisector of a given straight line | 81 |
PARALLELOGRAMS | 87 |
The locus of a point which is equidistant | 101 |
90 | 105 |
MISCELLANEOUS EXERCISES | 107 |
Area by counting squaressquared paper | 114 |
AREA OF TRIANGLE | 120 |
Equivalent triangles which have equal bases | 126 |
THE THEOREM OF PYTHAGORAS | 128 |
Projections | 136 |
MISCELLANEOUS EXERCISES | 145 |
COR A straight line drawn through the midpoint of | 153 |
CONSTRUCTION To inscribe a regular hexagon in a circle | 160 |
THE TANGENT | 166 |
94 | 225 |
AH | 226 |
If two triangles have one angle of the | 235 |
i The internal bisector of an angle of | 248 |
If a straight line stands on another straight | 257 |
If straight lines are drawn from a point | 264 |
INEQUALITIES | 273 |
96 | 293 |
Drawing to Scale | 299 |
307 | |
308 | |
311 | |
Heights and Distances | |
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Common terms and phrases
AABC altitude angles are equal base BC bisects Calculate centimetres centre chord circle of radius circles touch circumcircle circumference common tangent concyclic Constr construct a triangle Construction Proof cuts BC cyclic quadrilateral diagonal diameter divided Draw a circle drawn parallel equal circles equiangular equidistant equilateral triangle figure find a point fixed point Freehand given angle given circle given line given point given straight line hypotenuse inches interior angles intersect isosceles triangle LAPB length line joining locus of points Measure meet mid-point miles opposite sides parallel straight lines parallel to BC parallelogram Plot the locus polygon produced Pythagoras quadrilateral ABCD radii ratio reflex angle Repeat Ex rhombus right angles right-angled triangle segment set square Show similar triangles subtends THEOREM tracing paper trapezium triangle ABC vertex
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.