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10., , 11,, , 12., , 13., , 14., , 15., , 16., , 7., , 18., , QUADRILATERALS, , Prove that diagonals of rhombus bisect each other at right angle, , If diagonals of a quadrilateral bisect each other at right angle thon prove that it Is a, rhombus., , ABCD Is a parallelogram. If Its diagonals are equal, then find ABC., , Dlagonals AC and BO of a paraliclogram ABCD Intersect each other at If OA = 3m, and = OD = 2m, defermine the length af AC and BD, , In 4 ABC, AB = 5 cm, BC = 8 cm and CA = 7 cm. If D and E are respectively the, midpoints of AB and BC, determine the length of DE, , Dlagonals of a quadrilateral ABCD bisect each other If A= 35'delermine B, , The angles between two altitudes of a parallelogram through the vertex of an obtuse, angle of the parallatogram Is 60°. Find the angles of parallelogram, , ABCO Is a rhombus In which altitude from D to side AB bisects AB Find the angles of, the rhombus, , D, E and F are the midpoints of the sides BC, CA and AB, respectively of an equilateral, Irlangle ABC, Show that A DEF Is also an equilateral triangle., , Points P and Q have been taken on opposite sides AB and CD respectively of a, parallelogram ABCD such that AP = CQ. Show thal Ac and PQ bisect each other, , In a paraliclogram ABCD, AB = 10 cm and AD ~ 6 cm, The bisector af CA meets DC In, E. AE and BC produced meet al F. Find the length of CF., , P,Q. R and S are respectively the midpalnts of sides AB, BC, CD and DA of a square, ABCD then prove that PORS Is a square, , ABCD Is a quadrilateral In which AB 1 OC and AD = BC. Prove thal A= Band C=, D., , {na quadrijaterat ABCD, the line segments bisecting LC and LD meet at E. Prove that, A+ B= 2LCED, , The sides BA and DC of quad. ABCD are produced Prove that x+y =a3+b, oD c F, , b*, E A 8, , ABCD Is a parallelogram and x, y are the points on diagonal BD such that DX = BY., Prove that CXAY Is a parallelogram., , ABCD |s a parallelagram, E is mid-point of AB. DE and CE are Joined, CE bisects, LBCD.Provethat (l)AE=AD (jl) DE bisects LADC. (il) LDEC = 90°, , Stale and prove mid-point theorem.

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19., , 21., , 22., , 24,, , 26., , 27, , State and prove converse of mid-point theorem, , Prove that midpoint of hypotenuse of a right angled triangle Is equidistant from, vertices of a triangle, , Or, , Let ABC be a triangle, right - angled al B and D be the midpoint of AC. Show that, DA~ DB- DC, , Show that the figure formed by joining the midpoints of the adjacent sides of a, quadrilsteral ts a parallelogram, , Let ABCD be a trapezium in which AB 11 DC and let E be the midpoint of AD. Let F be, a point on BC such that EF Il AB Prove that, , (0) F Is the midpoint of BC (il) EF «(AB + OC), , Prove thal the Line segment joining the midpoints of the diagonals of a trapezium ts, parallel to the parallel sides and equal to half of thelr difference, , ABCD 5s a parallelogram in which P ts the midpoint of DC and O |s a paint on Ac, , such that CQ = 4 AC, Also, PO when produced meets BC at R prove that R ts the, midpoint of BC, , ABCD Is # trapezium in which AB 1 DC and AD « BC, If P.O, R, Sbe respectively, the midpoints of BA, BD and CD , CA then show that PORS is a rhombus., , AD |s a median of A ABC and £ is the midpoint of AD Also BE produced meets AC In, F, prove that AF SAC, , DE. F are the midpoints of the sides BC , CA and AB of AABC If BE and DF, Intersect at X while CF and DE Intersect at Y. Prove that XV - % BC, , Prove thal line Joining the midpoints of non-paraltel sides of a trapezium is parallel to, the paraitel sides and half of the sum of them, , ABCD Is a rhombus BC is produced to E and F on both sides. AE and DF are joined, and produced to intersect at G such thal BE = BC = FC. Prove that LEGF = 90°, , In the given figure ABCD is a square and EF 11 BD. M |s midpoint of EF. Prove that, AM bisects LBAD., , A 5, , =\, , , , 8 E c 0