Question
In a triangle ABC, D, E and F are the mid-points of the
sides BD, CA and AB, respectively. BE and DF intersect at X. DE and CF intersect at Y. Find XY = ?Solution
In ΔABC, F is the midpoint of AB and E is the midpoint of AC. ∴ By Midpoint Theorem, EF ∥ BC ∴ EF ∥ BD ----(1) ⇒ EF = BC/2 ----(2) Since D is the midpoint of BC, ⇒ EF = BD ----(3) From equation 1 and 3, ⇒ BDEF is a Parallelogram. BE and DF intersect at X. Similarly, DCEF is a Parallelogram. DE and CF intersect at Y. ∵ X and Y are the midpoints of sides DF and DE, respectively. In ΔDEF, X is the midpoint of DF and Y is the midpoint of DE. ∴ By Midpoint Theorem, ⇒ XY = EF/2 ----(4) From equation 3 and 4 ⇒ XY = BC/4
A) dismal B) Appellant C) Plaintiff D) Vile
...Select the most appropriate antonym of the given word.
BOLD
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Choose the word that means the same as the given word.
Quandary
Perpetual
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Appearance
DEMEAN
Each of the following questions consists of two words which have a relationship to each other. This is followed by four pairs of related words. Choose t...
She is optimistic about her future.
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