Question

In $\Delta$ ABC, DE is parallel to BC. Which of the following are correct?

• A. $\frac{1}{2}\text{× Area of BDEC = Area of ΔBDC}$
• B. Area of ∆BEC and ∆ BDC are equal.
• C. Area of ∆DOB= Area of ∆EOC
• D. Area of ∆DOB= Area of ∆EOD

Answer 1

Answer: (B), (C)

The correct options are
B Area of ∆BEC and ∆ BDC are equal.
C Area of ∆DOB= Area of ∆EOC

Area of ∆BEC and ∆BDC will be equal as they are on the same base (BC) and between same parallel lines (BC and DE).
$\therefore$ Area of $\Delta$ BEC = Area of $\Delta$ BDC ...(i)

$\Rightarrow$ Area of ∆BEC - Area of ∆BOC = Area of ∆BDC - Area of ∆BOC.
$\Rightarrow$ Area of ∆DOB = Area of ∆EOC. (Observe from the figure)