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Radius or Radii. Diameter. Arc. Sector. Chord. Segment. Centre.

Terms which you will need to be familiar with are:[br] [b]Locus[/b]: A line or region that indicates all of the points which fit a specific rule.[br] [b]Loci[/b]: The plural of Locus[br] [b]Equidistant[/b]: A collection of two or more points that are of equal distance from one another.[br] [b]Perpendicular[/b]: Two lines that are at right angles to one another.[br] [b]Bisect[/b]: A line or measured distance that is divided in two.[br][br]The worksheets in this chapter will give you details on how to construct the four different types of Loci. You should practice drawing Loci. In order to do that correctly ensure that you use a ruler and compass (and pencil!).[br][br]Links to Loci types:[br][url=https://www.geogebra.org/m/KyAkHRV6]Loci Type 1[/url][br][url=https://www.geogebra.org/m/AxArfYj2]Loci Type 2[br][/url][url=https://www.geogebra.org/m/Tk9hqYUx]Loci Type 3[br][/url][url=https://www.geogebra.org/m/kAba9dBk]Loci Type 4[/url][br]

How do we define a ratio as something that is simple to understand? A ratio is defined as a proportion of one "thing" to a proportion of something else. This is expressed as 1 : [i]n[/i] where [i]n [/i] can be any value.[br][br]As an example we could have Lemons and Oranges as a ratio of 1 : 7 [br]What this means is that for every 1 Lemon we have 7 Oranges.[br]Take a look at the graphic below for an in depth explanation.

Pythagoras gets everywhere in Maths. [br][br]The rules of the Right Angled Triangle will form the basis of a reasonable amount of work that you will do within the curriculum in terms of geometry.[br][br]a[sup]2 [/sup]+ b[sup]2 [/sup]= c[sup]2[br][br][size=100]Length a squared + Length b squared = Length c squared[/size][br][/sup]This applies only within Right Angled Triangles. You can disprove that a triangle has a right angle based on the above rule.

Here is a worked example of how to convert a decimal number to a fraction and then simplifying it.[br]Write 0.796 as a fraction. To do this we need to convert the .796 into a numerator and the denominator is the integer "1" followed by a number of zeroes that are equal to the number of decimal places. There are three decimal places in .796 so there are three zeroes after the number "1" (essentially what we are doing is removing the decimal point by multiplying by 1000).[br][br][img width=47,height=50]data:image/png;base64,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[/img][br][br]Simplify the fraction using Prime Factorisation[br][br]796 = 2 x 2 x 199 = 2[sup]2[/sup] x 199[br]1000 = 2 x 2 x 2 x 5 x 5 x 5 = 2[sup]3[/sup] x 5[sup]3[br][br][img width=201,height=53]data:image/png;base64,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[/img][br][br][size=100][size=150]Indices in the numerator and denominator cancel each other out.[/size][/size][br][br][img width=226,height=50]data:image/png;base64,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[/img][br][br][/sup]

C.I.A. - This is not the Central Intelligence Agency! This acronym will help you to understand angles on parallel lines.[br][br]C - corresponding angles[br]I - Interior angles (or supplementary angles)[br]A - Alternate angles[br][br]Take a look at the graphic below.[br]Corresonding angles are marked in green.[br]Interior angles are marked in red.[br]Alternate angles are marked in blue.[br][br]Corresponding angles are always equal (on a parallel line).[br]Alternate angles are always equal (on a parallel line)[br][br]Interior angles (on a parallel line) always add up to 180[math]^\circ[/math]