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Question

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


  1. Area of ∆BEC and ∆ BDC are equal.

  2. (1/2)Area of BDEC = Area of ∆BDC

  3. DE is parallel to BC

  4. All of the above


Solution

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=12 BC (mid point theorem)

(iv) area Δ BDE = area Δ CED

(Δ's on the same base and between the same parallels)

area Δ DOB + area /Δ DOE=/area ΔDOE + area Δ EOC

area Δ DOB = area Δ EOC

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