### 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 informati