Angle Rules

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# Angle Rules - PowerPoint PPT Presentation

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 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

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## PowerPoint Slideshow about 'Angle Rules' - kermit

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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

The complement of 55o is 35o because these add to 90o

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

#11

x

x

x

x

x

### Lesson 6

Circle Language and Angle at Centre

x

Base ‘s isos Δ, = radii

Base ‘s isos Δ, = radii

Sum of Δ = 180°

*

### 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

A quadrilateral which has all four vertices on the circumference of a circle is called a

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

#11

x

x

x

x

x

### 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 DOC = 68°.

Calculate the size of angle ABC.

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.

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.