Please do 2 and 4 question... le after completing chapter 4 of Geometry.
1. D is any point on AC in AABC. P, Q, X and Y are the midpoints of
AB, BC, AD and DC respectively. Show that PX = QY.
2. In a ,MBC, AD is a median and E is the midpoint of AD. BE is
joined and produced to meet AC at F. Prove that AF = — AC.
3. In AABC, AD is perpendicular to the bisector of LB. DE is drawn parallel to BC to meet AC at E.
Prove that AE = EC.
4. Prove that the sum of the squares on the three sides of an equilateral triangle is equal to four times
the square on a median.
5. Prove that the sum of the squares on the sides of a parallelogram is equal to the Sum Of the squares
on the diagonals.
6. ABCD is a square. The points P, Q, R and S are taken on AB, BC, CD and
DA respectively, so that AP = BQ —CR DS Prove that
(a) PQRS is a square
(b) = PQ2
(c) -2(AP2 + BP2)
[ÉE.J Shot on OnePlgy
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