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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).

A

Area of ∆BEC and ∆ BDC are equal.

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B

(1/2)Area of BDEC = Area of ∆BDC

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C

DE is parallel to BC

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D

All of the above

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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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