Q9 of 31 Page 232

D is the midpoint of side BC of triangle ABC Parallelogram CDEF stands between side BC and parallel to BC through the point A. Let’s prove that triangle ABC = parallelogram CDEF.

Given.


D is the midpoint of side BC of triangle ABC Parallelogram CDEF stands between side BC and parallel to BC through the point A


Formula used.


Area of triangle = × Base × Height


Area of parallelogram = Base × Height



In triangle ABC


Area of triangle ABC = × Base × Height


Area of triangle ABC = × BC × AX


In parallelogram CDEF


Area of parallelogram CDEF = Base × Height


Area of parallelogram CDEF = DC × AX


⇒ height of both parallelogram and triangle will be same


Because of stands on BC and parallel through point A


As D is mid-point of BC


DC = × BC


⇒ 2×DC = BC


Area of triangle ABC = × BC × AX


= × 2 × DC × AX


= DC × AX


= Area of parallelogram CDEF


∴ triangle ABC = parallelogram CDEF


More from this chapter

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7

E is any point on side DC of parallelogram ABCD, produced AE meets produced BC at the point F. Joined D, F. Let’s prove that

(i) triangle ADF = triangle ABE


(ii) triangle DEF = triangle BEC.

 8

Two triangles ABC and ABD with equal area and stand on the opposite side of AB let’s prove that AB bisects CD.

 10

P is any a point on diagonal BD of parallelogram ABCD. Let’s prove that triangle APD = triangle CPD.

 11

AD and BE are the medians of triangle ABC. Let’s prove that triangle ACD = triangle BCE.