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Show that the diagonal.s of a parallelogram divide it into four triangles of equal area.

Show that the diagonal.s of a parallelogram divide it into four triangles of equal area.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 8741 Points
8 months ago
Construction: Draw DL perpendicular t.o AC. Proof: We know that diagonals of a c parallelogram bisect each other. i.e., OA = OC and OB = OD ...(i) A ar(AOD) = 2 x AO x DL 130 ar(DOC) = 2 x OC x DL ...(iii) From (i), (ii), (iii ), we get ar(AOD) = ar(DOC) ...(iv ) Similarly, by drawing perpendiculars from C and B on BD and AC respectively, we can show that ar(DQC) = ar(COB) ...(v ) and ar(BOC) = ar(AOB) ...(vi) From (iv ), (v) and (vi), we get ar(AOB) = ar(BOC) = ar(COD) = ar(AOD).

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