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Showing posts from October, 2010

### Geometrical Proofs Introduction

Intercept theorem
There are 2 ways to apply the intercept theorem

In the first scenario, you will be able to identify a pair of parallel lines from the question
Upon identifying the pair of parallel lines,
we conclude that the ratio of AD:DB is the same as the ratio of AE:EC

In the second scenario, you identify that that the ratio of AD:DB is the same as the ratio of AE:EC
Subsequently you conclude that the lines DE and BC are parallel

Midpoint Theorem
The Midpoint theorem is a specific case of the Intercept theorem when the ratio of the lengths is 1:1

There are 2 ways to apply the Midpoint Theorem

The first way is to use Midpoint Theorem to show that 2 lines are parallel
From the information given in the question, we will be able to identify that D is the midpoint of AB and E is the midpoint of AC
Given that D and E are midpoints, we will be able to conclude that DE is parallel to BC

The second way is to use Midpoint Theorem to show that E is a midpoint
From the information given in th…