Constructions
1. Bisector of a given angle using a compass and a straight edge 2. Perpendicular bisector using a compass and straight edge
3. Line perpendicular to a given line l, passing through a given point not on l 4. Line perpendicular to a given line l, passing through a given point on l 5. Line parallel to given line, through given point
6. Division of a line segment into three equal segments, without measuring it 7. Division of a line segment into any number of equal segments, without measuring it 8. Line segment of a given length on a given ray
9. Angle of a given number of degrees with a given ray as one arm 10. Triangle, given lengths of three sides
11. Triangle given two sides and the angle in between them (SAS) 12. Triangle, given two angles and the side in between them (ASA)
13. Right-angled triangle, given the length of the hypotenuse and one other side 14. Right-angled triangle, given one side and one of the acute angles 15. Rectangle, given the side lengths
Theorems 1. Vertically opposite angles are equal in measure. 2. In an isosceles triangle, the angles opposite the equal sides are equal.
Two lines are parallel if and only if for any transversal, corresponding angles are equal. 6. Each exterior angle of a triangle is equal to the sum of the interior opposite angles. 9. In a parallelogram, opposite sides are equal and opposite angles are equal. 10. The diagonals of a parallelogram bisect one another.
3. If a transversal makes equal alternate angles on two lines, then the lines are parallel. 4. The angles in any triangle add to 180 degrees. 5.
11. If three parallel lines cut off equal segments on some transversal line, then they will cut off equal segments on any other transversal.
12. Let ∆ABC be a triangle. If a line t is parallel to BC and cuts [AB] in the ratio m:n, then it also cuts [AC] in the same ratio.
13. If two triangles are similar then their sides proportional, in order.
14. Pythagoras’s theorem: In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
15. Converse of Pythagoras’s theorem: If the square of one side of a triangle is the sum of the squares of the other two, then the angle opposite the fi rst side is a right angle.
19. Circle theorem: The angle at the centre of a circle standing on a given arc is twice the angle at any point of the circle standing on the same arc.
number 145
145 147 145
145, 147 287 287 145 145 145 145 145 145 145 145
Page
number 149
149 149 149 149 149 149 149 289
290 296 149, 305 149 331
Page
Linking Thinking 2 revision index Formulae
Page number
Number Compound interest Laws of indices Net tax
Percentage increase or decrease Percentage profi t/loss
Percentage profi t margin and mark-up
Geometry and trigonometry – 2D shapes and 3D solids Area
Perimeter/Circumference Pythagoras’s theorem Surface area
Trigonometric ratios Volume
Geometry and trigonometry – Coordinate geometry Distance between two points Equation of a line Midpoint Slope
Slopes of parallel lines Slopes of perpendicular lines
Algebra and functions General term for quadratic patterns Linear functions Quadratic formula
Statistics and probability Expected number of outcomes Fundamental principle of counting Mean
Median Mid-interval value
Probability of an event happening Range
Relative frequency 272
212–220 276 82 79 84
56 56
149, 304, 305 68, 72, 259 309
63, 64, 67, 72, 259
163 340 158
166, 167, 344 170, 341 171, 342
186 47
243
94 89
15, 16, 129 14
129 89 16 93
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