### 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…

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…