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AS 1.6 Geometric Reasoning AS91031

1.6 Geometry Home | Objectives | Angles | Angles & Lines | Triangles | Parallel Lines | Polygons | Interior & Exterior Angles | Polyhedra | Similar Triangles | Circles | Proofs | Revision

Summary: 4 Credit External Assessment

Angle properties of intersecting and parallel lines and properties of polygons.
Similar shapes & using proportion to find unknown side lengths.
Using pythagoras in 2 and 3 dimensions.
Using trigonometry in 2 and 3 dimensions.
Using angle properties relating to circles.

  • Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties.
  • Recognise when shapes are similar and use proportional reasoning to find an unknown length.
  • Use trigonometric ratios and Pythagoras’ Theorem in two dimensions.
  • Deduce and apply the angle properties related to circles.

 

 

 

Starters

Geogebra Java Manipulatives

 
1



Overview and Basic Angle Rules

Review of Angles.
Basic geometric rules:
Angles on a line add to 180. Opposite angles are equal. Angles at a point add to 360. Angles in a triangle add to 180.

 

Achievement Standard

Overview | Class notes, Blank notes

 

Overview | Measuring Angles | Angle rules 1

Opposite Angles | Angles on a line | Angles at a point

2



Angles in Triangles

The sum of angles in triangles: scalene, isosceles, equilateral.

Class notes, Blank notes

Ex 31.01 p448
(Ex 31.02 p451)

 

Angles in Triangles

Angles in a triangle | Isosceles Triangle

3



Parallel Lines

Corresponding Angles equal, Co-interior angles add to 180, Alternate angles are equal

Class notes, Blank notes

Parallel line rules Ex 31.03 p453
Practice Ex 31.04 p454
Harder Problems Ex 31.05 p456

 

Parallel Lines

p128

Corresponding | Two Corresponding | Alternate | Cointerior

4



Are Lines Parallel?

Using parallel line rules to determine if lines are parallel

Ex 31.06 p457

 

5



Polygons

Interior & exterior angles.
Sum of Exterior angles in a polygon
Sum of Interior angles in a polygon

Class notes, Blank notes

Ex 31.07 p461 Ex 31.08 p464

 

Polygons

p129

Exterior Angles

6



Quadrilaterals

Names and properties of quadrilaterals
Describing quadrilateral properties
Rotational Symmetry. Reflective Symmetry. Total order of symmetry



Class notes, Blank notes

Ex 32.01 p468

 

Rectangle |

7



Finding angles in Quadrilaterals

Solving angle problems involving quadrilateral properties

Ex 32.02 p470

 

p130

8



Similar Triangles

Definition of similar triangles.
Solving problems involving similar triangles

Class notes, Blank notes

Ex 32.03 p473

p132

Similar Triangles

9



Circles

Definitions of radius, diameter, chord, arc, sector, segment, circumference, tangent.
Two radii form an isosceles triangle.
Angle in a Semicircle is 90
Angle at centre is twice angle at circumference

Class notes, Blank notes

Circle parts Ex 33.01 p476
Circle angle problems Ex 33.02 p479

Isosceles triangle | Angle in a semicircle | Angle at centre

10



Angles on Same Arc, Cyclic Quadrilateral

Proof of angles on same arc are equal.
Opposite angles in a cyclic quadrilateral add to 180

Class notes, Blank notes

Angles on Same Arc Ex 33.03 p481
Cyclic Quadrilaterals Ex 33.04 p483

p133

Angles on same arc | Cyclic Quadrilaterals

11



Concyclic points

Definitions of collinear, concyclic,
circumference

Class notes, Blank notes

Ex 33.05 p476

p134

 

12



Circle Tangents

Definitions of tangent. Tangent and radius are perpendicular

Ex 33.06 p487

p135

Radius and tangent

13



Using Algebra in Geometry

Using geometric reasoning and algebra to solve problems.

Class notes, Blank notes

Ex 33.08 p490

p136

14



Geometric Proofs

Using geometric reasoning to follow a chain of reasoning and solve problems.

Class notes, Blank notes

Ex 33.09 p491

p137

15



Geometry Terms

Review of geometric rules and vocabulary

Class notes, Blank notes

Ex 31.08 p464 | Ex 33.07 p489

p127

16



Revision

Practice assessments

Class notes, Blank notes

Practice test p494

p138

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