A plot is in the form of rectangle abcd.Owner of this plot wantbto build old age home,dispensary,park and healthcentre for elderly people as shown in fig.P is the midpoint on diagonal bd.Prove that area alloted to old age home and healthcentre are congruent.
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As it is a rectangle, so AD=BC.
Also, p is midpoint of BC. So, BP=PD.
As AD is parallel to BC, angle ADP=angle CBP. Thus by SAS, triangles are congruent and have equal areas.
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