A b c d e a b c. a b c d a b c a c b d Complementary Angles add to 90 o The complement of 55 o is 35 o because these add to 90 o Supplementary Angles.

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Presentation transcript:

a b c d e a b c

a b c d a b c

a c b d Complementary Angles add to 90 o The complement of 55 o is 35 o because these add to 90 o Supplementary Angles add to 180 o The supplement of 55 o is 125 o because these add to 180 o C before S 90 before 180

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Rules of Parallel Lines

x

a

a

No of sides NameNo Of Degrees in polygon Each interior angle for regular polygons (sides are equal) Sum of exterior angles 3Triangle 4Quadrilateral 5Pentagon 6Hexagon etc 12Dodecagon ×2 = ×3 = ×4 = ×10 = ÷3=60 360÷4=90 540÷5= ÷6= ÷12=

For regular polygons only For ANY polygon For regular polygons only

Degrees in the polygon : x 95 x

This is a regular 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

* Base ‘s isos Δ, = radii x Sum of Δ = 180°

Angle at the centre is twice the angle at the circumference a a a a 2a

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

Tangent is perpendicular to the radius

Angles on the same arc are equal ‘s On the same arch equal

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Find unknowns and give reasons *

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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

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* Find unknowns and give reasons

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Tangents When two tangents are drawn from a point to a circle, they are the same length

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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

Revision

Geometric reasoning revision

2006 exam QUESTION ONE The diagram shows part of a fence. AD and BC intersect at E. Angle AEB = 48°. Angle BCD = 73°. Calculate the size of angle CDE. QUESTION TWO The diagram shows part of another fence. LM = LN. KL is parallel to NM. LM is parallel to KN. Angle LNK = 54°. Calculate the size of angle LMN.

2006 exam The points A, B, C and D lie on a circle with centre O. Angle OAD = 55°. Angle DOC = 68°. Calculate the size of angle ABC. You must give a geometric reason for each step leading to your answer.

QUESTION THREE The diagram shows the design for a gate. AE = 85 cm BE = 64 cm CD = 90 cm Triangles ABE and ACD are similar. Calculate the height of the gate, AD.

QUESTION FOUR The diagram shows a design for part of a fence. GHIJK is a regular pentagon and EHGF is a trapezium. AB is parallel to CD. Calculate the size of angle EHG. You must give a geometric reason for each step leading to your answer.

QUESTION FIVE The diagram shows another fence design. ACDG is a rectangle. Angle CBA = 110°. CG is parallel to DE. DA is parallel to EF. Calculate the size of angle DEF. You must give a geometric reason for each step leading to your answer.

In the above diagram, the points A, B, D and E lie on a circle. AE = BE = BC. The lines BE and AD intersect at F. Angle DCB = x°. Find the size of angle AEB in terms of x. You must give a geometric reason for each step leading to your answer.