We can see a triangle ABC. D and E are the mid points of the sides AB and AC respectively. m and m_1 are the slopes of the line segment BC and DE respectively. Observe how the shape of the triangle and values of m and m1 get changed when we move the points A, B and C. Also observe the lengths of the line segments BC and DE.

Questions to think about[br]1. Move the points A, B and C, what is the relationship between m and m1? [br]2. Is it possible to have m≠m1?[br]3. Move the points A, B and C, what is the relationship between the lengths of BC and DE?