similar triangles

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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Length of video = 11 minutes.

[Video] E-Math Popular Exam Question: Finding Ratio of Areas in Vectors (Includes 3 Strategies & Revision of Similar Triangles)

In this post, we are going to discuss on the applications of vectors - Finding Ratio of Areas. This is a popular section in examinations and based on my many years of experience, students simply don't like it due to many of them disliking and not making sense of the topic on Similar Triangles.

Strategy #1 : Similar Triangles

In Similar Triangles, the ratio of 2 similar triangles can be easily found by squaring the ratio of their corresponding length.

[pmath]({A_1}/{A_2})=({l_1}/{l_2})^2[/pmath]

Strategy #2 : Common Base/Common Height

I am going to use this examination question below to illustrate the application of Strategy #2. This strategy works when the triangles shared either a common base or a common height. And that the triangles are not similar.

Watch the video below to find out if your answers are correct. Included in this video is a trick which will help you to 'see' your answer faster!

Rate the video or leave me a comment or question.

Strategy #3 : Overlap

When strategy 1 or 2 do not work and the question involves repeated triangles, overlap is the strategy you can apply. Overlap involves equalizing of ratio of THE triangle which overlaps.

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