• Mathematics Extension 1
• Year 11

# Plane and Circle Geometry

approx. 16 hrs

8 topics

42 concepts

Develop mastery of Plane and Circle Geometry and maximise your HSC results in Mathematics Extension 1.

Available in
NSW

### Overview

This learning program covers the essential components of the Year 11 Mathematics Extension 1 Plane and Circle Geometry topic as outlined the NSW syllabus.  We help students gain competence in understanding congruence and similarity and its application to geometrical proofs. This includes providing deductive reasoning and geometrical justification for each step. In addition, we focus on selecting and applying appropriate circle theorems to solve geometrical proofs.

### Topics & Concepts We Cover

This learning program is made up of the following 8 topics, broken down into 42 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. Investigate and apply the exterior angle of a triangle property to find angles in a given diagram

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

3. Apply Exterior Angle Sum of Polygons

4. Apply the Interior Angle Sum of a Polygon formula

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 9 concepts

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

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

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

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

5. Scaling ratio for volume

6. Scaling ratio for area

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

8. Tests for similar triangles

9. Prove and apply tests for quadrilaterals using similarity results

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

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

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

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

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

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

1. Proving Quadrilaterals are Cyclic

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

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

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

5. The Tangent-Secant Theorem

6. Tangents from an external point are equal.

### 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 be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime