• Mathematics Specialist
• Year 11

# Plane and Circle Geometry

approx. 16 hrs

8 topics

44 concepts

Master Plane and Circle Geometry to maximise your results and advance into year 12 with confidence.

Available in
NT QLD SA TAS VIC WA

### Overview

Plane and Circle Geometry draws on prior knowledge of angle relationships and plane shapes. We provide students with an in-depth analysis of polygons and circles as described in the Mathematics Specialist Syllabus for the Australian curriculum. This program covers the concepts of congruence and similarity to prove geometric properties of a range of complex shapes. In addition, we help students develop knowledge and skills with circle theorems to construct logical proofs, justifying by using geometrical reasoning.

### Topics & Concepts We Cover

This learning program is made up of the following 8 topics, broken down into 44 concepts.

• #### Angle relationships 4 concepts

1. Apply rule that if two lines are parallel to a third line then they are parallel to one another

2. Use angle relationships to identify parallel lines

3. Find angles at a point using angle relationships

4. Use angle relationships of parallel lines to find the size of unknown angles, giving reasons

• #### Angles of Polygons 6 concepts

1. Apply Exterior Angle Sum of Polygons

2. Apply the Interior Angle Sum of a Polygon formula

3. Investigate and use the angle sum of a triangle property to find angles in a given diagram

4. Investigate and apply the exterior angle of a triangle property to find angles in a given diagram

5. Apply the triangle inequality rule

6. Find unknown sides and angles in a given diagram by using the properties of special triangles and quadrilaterals

• #### Congruence and Similarity 11 concepts

1. The golden ratio and the geometric mean

2. Application of the golden ratio

3. Prove and apply tests for quadrilaterals using similarity results

4. Apply the intercepts and parallel lines properties to find unknown sides

5. Application of congruent triangles to prove properties of special triangles and quadrilaterals

6. Choosing a test for congruence (SSS test, SAS test, AAS test, RHS test)

7. Write formal proofs of congruence of triangles, preserving matching order of vertices

8. Write formal proofs of similarity of triangles, preserving matching order of vertices

9. Tests for similar triangles

10. Scaling ratio for area

11. Scaling ratio for volume

• #### Pythagoras' Theorem 2 concepts

1. Prove Pythagoras' theorem using similarity

2. Converse of Pythagoras' theorem

• #### Circle Geometry - Arcs and Chords 5 concepts

1. Equal chords subtend equal arcs on a circle, and conversely

2. A line through the centre of a circle perpendicular to a chord bisects the chord, and conversely

3. Chords equidistant from the centre of a circle are equal, and conversely

4. Equal arcs subtend equal angles at the centre of a circle, and conversely

5. Equal chords subtend equal angles at the centre and conversely

• #### Circle Geometry - Angles in Circles 6 concepts

1. Angles at the circumference in the same segment are equal, and conversely

2. The angle between a tangent and a chord equals the angle at the circumference in the alternate segment

3. A radius (diameter) of a circle is perpendicular to the tangent at their point of contact

4. The angle at the circumference in a semi-circle is 90°, and conversely

5. The angle at the centre is twice the angle at the circumference standing on the same arc

6. Equal arcs subtend equal angles at the circumference, and conversely

• #### Circle Geometry - Cyclic Quadrilaterals 4 concepts

2. The exterior angle of a cyclic quadrilateral equals the interior opposite (or remote) angle, and conversely

3. The opposite angles of a cyclic quadrilateral are supplementary, and conversely

4. Proving Concyclicity

• #### Circle Geometry - Tangents and Intercepts 6 concepts

1. Application of circle theorems

2. Tangents from an external point are equal.

3. The Tangent-Secant Theorem

4. The products of the intercepts of two intersecting chords are equal, and conversely

5. The products of the intercepts of intersecting secants are equal

6. The line joining the centers of two circles passes through their point of contact

### What you'll get

Learning Content

• A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
• All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

• We match you to a private, expert tutor who is right for your needs and goals
• Our tutors are talented, tested, top ATAR achievers and subject experts
• During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Plane and Circle Geometry

Reporting

• Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
• You and your parents receive a comprehensive feedback report after every session
• Every session is recorded and available for you to watch at any time, allowing you to review what was covered

### Ready to start this program?

Simply pick a time that works for you

We'll book in your first session and match you to an expert tutor

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime