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## Angle Rules

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**b**a c e a d c b Angle Rules**b**a c c b a d**b**a c d Complementary Angles add to 90o The complement of 55o is 35o because these add to 90o Supplementary Angles add to 180o The supplement of 55o is 125o because these add to 180o C before S 90 before 180**1**180÷3=60 360 180 180×2 =360 360 2 360÷4=90 180×3 =540 3 360 540÷5=108 180×4 =720 720÷6=120 4 360 360 180×10 =1800 1800÷12=150 10 360**For ANY polygon**For regular polygons only For regular polygons only**155**135 130 x 95 x 80 135 130 95 135 Degrees in the polygon: Degrees in the polygon :**Similar Triangles**If triangles are similar: Corresponding side lengths are in proportion. (One triangle is an enlargement of the other) Corresponding angles in the triangle are the same 25m 20m x 4 m It doesn’t matter which way round you make the fraction BUT you must do the same for both sides It is sensible to start with the x so it is on the top**If the angles of two triangles are the same,**they are similar triangles.**#11**x x x x x**Lesson 6**Circle Language and Angle at Centre**Equal Radii: Two radii in a circle always form an isosceles**triangle Isos , = radii**x**Base ‘s isos Δ, = radii Base ‘s isos Δ, = radii Sum of Δ = 180° ***Angle at the centre is twice the angle at the circumference**a a 2a 2a 2a 2a a a**Angle on the circumference of a semicircle is a right angle**in semi-circle**Lesson 7**Tangent is perpendicular to the radius and Angles on Same Arc are equal**Angles on the same arc are equal**‘s On the same arch equal**Cyclic Quadrilaterals**A quadrilateral which has all four vertices on the circumference of a circle is called a Cyclic quadrilateral Rule 1:**Rule 2:**The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle**Tangents**When two tangents are drawn from a point to a circle, they are the same length**Similar Triangles**If triangles are similar: Corresponding side lengths are in proportion. (One triangle is an enlargement of the other) Corresponding angles in the triangle are the same 25m 20m x 4 m It doesn’t matter which way round you make the fraction BUT you must do the same for both sides It is sensible to start with the x so it is on the top**If the angles of two triangles are the same,**they are similar triangles.