plane geometry

A-Maths: Plane Geometry Question (Step-by-Step) [Video]

In this video, I will show you:

How to prove that 2 lines are // to each other
How to prove a pair of similar triangles
How to prove an equation involving length

Properties & Theorems used:

Angles in the same segment
Intercept Theorem
Corresponding angles
Tangent - Secant Theorem

Strategies (Used in manipulation in part iii) :

Breaking a longer length into smaller parts
'Expansion' of length
Using result from earlier parts
Factorising common length

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Link to video: http://www.youtube.com/watch?v=UNZolJverww

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Length of video = 11 minutes.

A-Maths: Plane Geometry (Geometrical Proof) Mastery Workshop + SPECIAL CODE

Student 1: "I can't see!"

Student 2: "I don't know how to start. I don't know which theorem or formula to use."

Student 3: "I always can't do plane geometry question in exams!"

Student 4: "I don't understand the topic at all!"

These are the common problems faced by many A-Maths students in the topic of Plane Geometry, even A-grade students!

Every year since 2008 in GCE O-Level Additional Maths Paper 2, there's always a Plane Geometry question worth 8 to 10 marks!

This topic can be made easier by

Looking out for hints given in the question and diagram
Understanding the newly introduced theorems (5 of them)
Combining E-Maths angle and symmetry properties of circle
Learning the 'dummy-proof' way to prove congruent and similar triangles
Exposure to a variety of strategies and questions
Learning how to apply the skills learnt on solving questions

I'm conducting my final A-Maths Mastery Workshop on Plane Geometry this September!

Join me for this final revision and solve that Plane Geometry question in O-Level 2013, add 10 marks to your final score!

For more details: go to www.singaporeolevelmaths.com/pg

Enter special code to enjoy $28 discount off the workshop fee!

Video Solution Of Plane Geometry Question (Plus:Strategy To Handle Angles)

This is the step by step video solution for this Plane Geometry question

Inside this video, you will get to know how I begin this question with a clear objective and the steps I took to achieve this objective.

I used 2 strategies (on differentiating the angles) to quickly and easily prove this question.

Letting an angle be x
Usage of color (In exams, you can perhaps use different type of lines to differentiate the angles as well)

Hear from you on this approach. If you have your own approach, we would love to hear from you.

Leave me a comment in the section below.

A-Math: This Plane Geometry Question Almost Drives Me To Insanity!

Plane geometry is one of the top killer questions in A-Math as there are many things to prove in addition to the many lines, circles, triangles, angles ...

Read about the post I wrote earlier What you need to know to do well in Plane Geometry Part 1

I must admit this question almost drives me to insanity ;-) but luckily I saw the light when I was on the verge of sane and insanity ...

Question: Prove that a circle can be drawn passing through the points T,P,X and Q. [3 marks]

planegeometry-circle

Let me know how you handle this question in the comments section. For those who wants the step by step solution, drop me a comment as well. I highly recommend that you think about this question first before asking for solution.

There are 2 strategies I have used to help me in this Plane Geometry question. Do you want to know? so that you can learn and use them in your own question.

Hint: You must use one of the properties of circles.

Update: Video solution Here

What You Need To Know To Do Well In Plane Geometry - Part 1

Plane Geometry is the new topic added in the new syllabus. There are hardly any calculations but lots of proving to be done.
We know students dislike proving, be it in Plane Geometry, Trigonometry, Quadratic Equations, Differentiation . . .

To score As in your exam, you must be good in proving.

Plane Geometry has proven to be a challenging topic for many students due to the nature of the diagrams, questions. Many a times, students do not know when to begin, not to mention which theorems to apply. I am going to share with you in this post on the key concepts you need to know at your fingertips for Plane Geometry.

There are 2 basic shapes in Plane Geometry: Triangle & Circle

In Triangle,

You must know the different Congruency Tests & Similarity Tests. These are extremely important in proving plane geometry questions. Teachers did not emphasize on this as students are expected to know these concepts well from E-Math. But I realize many many students did not like Congruency & Similarity as it involves proving (which is a very systematic approach of thinking) and hence many did not understand these 2 concepts well.
Mid point theorem (This is not exactly your mid point formulae in Co-ordinate Geometry)

D and E are the midpoints of AC and AB respectively.

Intercept theorem

When DE//CB, AD/DC = AE/EB

I will be adding on specific properties for circle in my next post. If you like to be updated, subscribe to my feed by clicking HERE