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. (1/2)Area of BDEC = Area of ∆BDC
• C. DE is parallel to BC
• D. All of the above

Answer 1

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

The correct options are
A

Area of ∆BEC and ∆ BDC are equal.

C

DE is parallel to BC

D

All of the above

(i) D is midpoint of AB (given)

(ii) E is midpoint of AC (given)

(iii) DE || BC and $DE=\frac{1}{2}$ BC (mid point theorem)

(iv) area $\Delta BDE$ = area $\Delta CED$

($\Delta$'s on the same base and between the same parallels)

$\therefore$ area $\Delta DOB$ + area $\text{/}\Delta DOE=\text{/}\text{area}\Delta DOE$ + area $\Delta EOC$

$\therefore$ area $\Delta DOB$ = area $\Delta EOC$