Long Answer Type
ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that:
(i) D is the mid-point of AC (ii) MD ⊥ AC (iii) 
Short Answer Type
Prove that MN = 
Long Answer Type
D, E, F are respectively the midpoints of the sides BC, CA and AB of a triangle ABC. Show that:
(i) BDEF is a parallelogram
(ii) DFEC is a parallelogram.
Given: D, E, F are respectively the midpoints of the sides BC. CA and AB of a triangle ABC. To Prove:
(i) BDEF is a parallelogram
(ii) DFEC is a parallelogram.
Proof:
(i) In ∆ABC,
∵ F is the mid-point of AB and E is the mid-point of AC
∴ FE || BC | By mid-point theorem
⇒ FE || BD ...(1)
Again, In ∆ABC,
∵ D is the mid-point of BC and E is the midpoint of AC.
∴ DE || BA | By mid-point theorem
Short Answer Type
Long Answer Type
(AB + DC).
Switch
