Please help me out with this problem P and R are the mid-points of the sides AB and AC of AABC. BR and pc intersect at O. prove that ABOC quad. APOR.
y ABCD is a parallelogram. Two squares ABPQ and ADRS are drawn on the Sides AB and AD respectively outside the
16) BE and CF are the medians of LABC and G is their point of intersection. FEcuts AG at O. Prove that AO 306
ABCD is a parallelogram. X and Y are the mid-points of the sides AD and BC respectively. If P be any point on XY produced, prove that
AAPB parallelogram ABCD.
18) In a parallelogram ABCD, a straight line parallel to the side AB intersects AD, ACand BC or those line segmentproduced at E FandG
respectively. Prove that AAEG MFD.
a diagonal of a quadrilateral divides it into two triangles of equal areas, prove that it will bisect the other diagonal.
) D is the mid-point of the side BC of LABC P and Q are pointson the sides BCand BA respectively such that ABPQ = hABC, Prove that
21) P is any point on the diagonal BD ofthe parallelogram ABCD. Prove that AAPD = AC.PD in area.
22) D is any point on the side BC ofa triangle ABC. The straight lines drawn through the point D parallel toCA and BAintersect BAand CA at E
and F respectively. Prove that triangle FBD = triangle EDC, in area.
23) ABC and DBC are two triangles equal in area. They stand on the same base BC but lie on opposite side of it. AD intersects BC at prove that E
is the mid-point of AD.
24) O is a point outside the parallelogram ABCD and is in the region bounded by AB produced and DC produced. Prove that
MOD = MOB + NOD + ABOC in area.
25) Two triangles of equal area stand on the same base but on opposite side of it. Show that the Straight line joining their vertices is bisected by