Question

In $\Delta$ triangle ABC, D and E are the midpoints of side AB and AC. State which of the following are correct option(s).

• A. Area of ∆BEC and ∆ BDC are equal.
• B. $\frac{1}{2}$ Area of BDEC = Area of ∆BDC
• C. DE is parallel to BC
• D. Area of ∆DOB = Area of ∆EOC

Answer 1

Answer: (A), (C), (D)

Area of ∆DOB = Area of ∆EOC

D and E are the midpoints of AB and AC.
DE will be parallel to BC (Midpoint theorem).

Area of ∆BEC and ∆BDC will be equal as they are on the same base and between the same parallel lines.
Also, Area of ∆BEC - Area of ∆BOC = Area of ∆BDC - Area of ∆BOC.
Thus, Area of ∆DOB = Area of ∆EOC.